How is Kent similar to Lear in King Lear?

Both Kent and Lear are proud, headstrong, outspoken, and quick-tempered. Kent manages to get himself rendered homeless even before Lear or Gloucester. Kent impulsively jumps to Cordelia's defense when Lear disowns and banishes her, making her temporarily homeless too. Lear is the only one who opposes Lear's rash decision to disown his youngest daughter when she fails to flatter him with lies. Lear gets himself put into the stocks for impulsively attacking Oswald and then insulting Regan and her husband the Duke of Cornwall. He tells Cornwall:

Sir, 't is my occupation to be plain:
I have seen better faces in my time
Than stands on any shoulder that I see
Before me at this instant. 

Lear has the same temperament as Kent. In just a few moments in the opening scene of the play he gives his kingdom away, disowns Cordelia, and banishes Kent. Lear is so proud and headstrong that he even banishes himself! He refuses to make any sort of compromise with Goneril or Regan and rushes out into the open country at the worst possible time, with a storm brewing and night coming on. It is because of his rash and impulsive temperament that he has to remain homeless and destitute. He exists on anything he can find to eat, just like Edgar. At one point Lear apparently even seems to show that, rather than go to either of his daughters for food and shelter, he has been eating mice.

Look, look, a mouse! Peace, peace; this piece of toasted cheese will do 't.

We can get an idea of how Lear has been staying alive from what Edgar, pretending to be a lunatic derelict, says in Act 3, Scene 4:

Poor Tom, that eats the swimming frog, the toad, the tadpole, the wall-newt and the water, that in the fury of his heart, when the foul fiend rages, eats cow-dung for sallets, swallows the old rat and the ditch-dog; drinks the green mantle of the standing pool...

We pity both Lear and Kent, yet we admire them for their pride, courage, integrity, independence, and truthfulness. Shakespeare is showing us what happens to men who are too honest. It might be added that Cordelia has apparently inherited her father's headstrong and independent spirit. Fortunately for her, the French king admires her spirit and makes her his queen. 

King Lear is one of the most tragic of Shakespeare's characters. Kent is one of his most trusted adviser's at first. There are a couple of similarities between the two men.

King Lear valued loyalty above most things. He wanted loyalty from his people and his family, although he wasn't the greatest of leaders. Kent also valued loyalty and his loyalty to King Lear was the greatest of all. Even after Lear had him banished, Kent's loyalty never once faltered for his king. 

King Lear also valued love. He wanted to know who loved him most. King Lear adored his youngest daughter, Cordelia, but tested her love. She was banished, as well, when her answer didn't suit him. Kent also valued love. His love for King Lear was undying. He would lay down his life for Lear. 

"My life I never held but as a pawn, to wage against thine enemies, not fear to lose it, thy safety being the motive"

This quote, made by Kent about King Lear, shows how much he love the king. He was willing to die for him. After he was banished, his love remained the same. He disguised himself as another person, just so he could be near King Lear and keep him safe. His love and loyalty never faltered, even to the end. 

Kent was a minor character in the play, but he and King Lear were the most alike. Their values were so similar. Kent had no problem telling the king how he felt about things, though. When the king banished Cordelia, Kent jumped to her defense.

"Reverse they doom; and, in thy best consideration, cheque this hideous rashness; answer my life my judgement, thy youngest daughter does not love thee least, nor are those empty-hearted whose low sound reverbs no hallowness"

Here Kent is trying to show his love and loyalty to King Lear, but showing him that Cordelia was the only daughter who loved him. These are just a couple of examples of how Kent and King Lear are similar. 

How are Kent and The Fool similar and different in King Lear?

This is an interesting question. The King likes the Fool because he amuses him and keeps him company. He is somebody to talk to. The Fool likes the King because Lear protects him and provides for him. Lear has led a life of privilege because he was a prince and heir apparent and has become the king. The Fool probably led a dog's life until he was picked up by Lear on a whim and made into a court jester. Consequently, Lear knows little about reality, while the Fool is worldly wise because he has been trained in the School of Hard Knocks. The Fool understands people because he has seen their dark side. He has even seen Lear's dark side more than once. Lear doesn't really understand people because he has always been flattered and treated with the greatest respect. Lear naturally believes that everybody loves and admires him. He finds out the sad truth that most people only care about themselves. The Fool doesn't have to find this out; he knew it from his birth. Ironically, Lear has more to learn from the Fool than the Fool has to learn from Lear. The Fool follows Lear out into the cold, cruel world because he loves him--but also because he has no other recourse. If the Fool were to remain behind he would be in grave danger. At best, he would only be thrown out into the storm. Even if Lear is no longer in a position to protect and provide for him, the Fool is better off with the King than he would be on his own. At the same time, the Fool can also offer Lear some good advice about how to get along in his new impoverished and homeless situation, because that is the kind of situation the Fool was very familiar with. Misery loves company. In almost any play, there have to be at least two characters talking to each other because all the information conveyed to the audience has to be conveyed through dialogue except when a character is soliloquizing. A good example and a good drama to use for comparison with King Lear is Waiting for Godot. The playwright Samuel Beckett had to have two characters waiting for Godot in order to be able to provide information, such as it is, via dialogue. So he created the memorable Estragon and Vladimir, whose plight is very similar to that of Lear and the Fool.

Kent and The Fool actually share quite a bit in common. Both are loyal to King Lear and both are also loyal to Cordelia, albeit for different reasons. Kent logically sees the superficiality of Goneril and Regan but pleads with the king to see Cordelia's honesty. The Fool understands this reasoning as well, but his loyalty to Cordelia is also based on kinship with her, perhaps even love. When Lear calls for The Fool, a knight replies, "Since my young lady's going into France, sir, the fool hath much pined away" (I.iv.62-3). When Lear condemns Cordelia for failing to shower him with praises, it is Kent who sticks up for Cordelia and tries to reason with the king: 

Thy youngest daughter does not love thee least;
Nor are those empty-hearted whose low sounds 
Reverb no hollowness. (I.i.152-54) 

Despite being banished by Learn, Kent returns disguised and becomes a (new to Lear) servant to the king. The Fool is also loyal to Lear. He and Kent try to give Lear honest advice about his predicament. But the Fool is more playful and sarcastic. In Act One, Scene Four, he gives Kent a fool's cap because he thinks he would be a fool to follow a king with no power over his kingdom. Kent is dubious at first but eventually agrees with the Fool's assessment of Lear's mistakes. 

Kent goes to Regan on behalf of Lear. He actively tries to help Lear. The Fool, still loyal, plays a different role; often compared to the chorus in a Greek play. (The chorus would often comment to the audience what is occurring in the play. The chorus would give information that the other characters may be unaware of.) Kent is Lear's faithful friend and servant. The Fool is Lear's faithful friend and servant but he also acts as a prophet or a speaker of riddles, characteristic of the chorus. Kent is more direct in trying to get Lear to be reasonable. The Fool uses riddles and sarcasm to achieve the same ends. 

In King Lear, describe Kent's character. How is he similar to Lear?

As the drama opens, Kent is not very similar to Lear.  He serves Lear, but does so with an honesty and openness that Lear has shown unable to acknowledge. For example in the opening scene, Kent speaks of the selflessness with which he associates in his own service to Lear:  

My life I never held but as a pawn 
To wage against thine enemies; nor fear to lose it, 
Thy safety being the motive.

In the emotional setting of the First Scene of the First Act, such honesty is distinctive.  It is not a condition that Lear is able to understand or recognize because of where he is in terms of his identity and sense of self.  Kent is very open about his own sense of loyalty and honor throughout the drama.  This is seen in how he does not recoil and retreat from Lear even when he is banished. Rather, he serves Lear in disguise as Caius, someone who appears to be of lower distinction.  Lear operates in a world of moral and emotional disguise, as he fails to see that which is true.  Kent, however, takes a disguise in order to carry out what he sees as his duty and obligation.  In this, one notices how divergent Lear and Kent at the exposition of the drama.  

Where Lear and Kent find similarity exists in how Lear moves towards the reality of truth and moral honesty.  For Lear, this process takes time, but when he achieves it, the language and images Shakespeare has him employ in his speech is strikingly similar to Kent.  For example, in Act V, scene 3, Lear speaks to Cordelia with the type of language that reflects devotion and a sense of commitment:

No, no, no, no! Come, let’s away to prison.
We two alone will sing like birds i' th' cage.
When thou dost ask me blessing, I’ll kneel down
And ask of thee forgiveness. So we’ll live,
And pray, and sing, and tell old tales, and laugh
At gilded butterflies, and hear poor rogues
Talk of court news,

Royal Lear,
Whom I have ever honour'd as my king, 
Lov'd as my father, as my master follow'd, 
As my great patron thought on in my prayers-