I had to edit your original question as it contained several questions. Please remember that you are not allowed to ask multiple questions on enotes.

The wedding scene is in Act III scene 2 of this hilarious play that talks a lot about gender roles and marriage in society. You will be able to find out about the entire wedding if you re-read this scene. However, to respond directly to your question, we are not told what Katharina is wearing. We can imagine that she is wearing wedding clothes that are suitable to her social position. However, we do get a very precise description of the attire of Petruchio, as reported by Bondello:

Why, Petruchio is coming in a new hat and an old jerkin; a pair of old breeches thrice turned; a pair of boots that have been candle-cases, one buckled, another laced; an old rusty sword ta'en out of the town armoury, with a broken hilt, and chapeless; with two broken points; his horse hipped, with an old mothy saddle and stirrups of no kindred...

This is clearly part of Petruchio's strategy to "tame" his new wife. His bizarre attire pushes her beyond the limits of embarrassment and shame as Petruchio states that "To me she's married, not unto my clothes."