First of all, there are really no incorrect answers to this question. Likely, your teacher is looking for an in depth explanation of your thoughts and opinion. Therefore, in order to fully answer this question, you must do two things. First, define family. Second, provide examples for your answer.

Personally, I'd answer this question by saying that family consititutes the people in an individuals life who love, care for, and support that person unconditionally. It could also be added that people do not necessarily get to choosetheir family. According to this criteria, yes, both Jim and Tom become family for Huck.

Tom Sawyer is Huck's best childhood friend. This is shown in the very first chapter of the novel:

Now she had got a start, and she went on and told me all about the good place. She said all a body would have to do there was to go around all day long with a harp and sing, forever and ever. So I didn't think much of it. But I never said so. I asked her if she reckoned Tom Sawyer would go there, and she said not by a considerable sight. I was glad about that, because I wanted him and me to be together (chapter 1).

As an orphan, though Huck does not have any real brothers and does not understand what a traditional family feels like, he finds a brother in his friend Tom.

Then, Jim and Huck support one another in their journey along the river. A relationship that begins somewhat selfishly for each (self-survival) becomes one of friendship and brotherly love by the end of the novel. Both Huck and Jim prove this. Huck proves this in his promise to free Jim, and Jim does so simply in his ongoing sense of loyalty to Huck:

"Pooty soon I'll be a-shout'n' for joy, en I'll say, it's all on accounts o' Huck; I's a free man, en I couldn't ever ben free ef it hadn' ben for Huck; Huck done it. Jim won't ever forgit you, Huck; you's de bes' fren' Jim's ever had; en you's de ONLY fren' ole Jim's got now" (Chapter 16).

As you answer this question for yourself, I encourage you to come up with your definition of "family," and then find evidence to support it from the text.

In The Adventures of Huckleberry Finn, do Huck and Jim constitute a family?

I have had to edit down your question to only include one question, according to enotes regulations. This is a great question! One of the things that is really important to focus on in this novel is how the relationship between Jim and Huck changes as the novel progresses and Huck matures more and more. One of the key themes of the novel is the coming of age of Huck, and this is exhibited through his increasing understanding of the wrongness in slavery and his increasing affection for Jim.

It is certain, however, that from Huck's discovery of Jim on Jackson's Island with him, Jim plays an almost fatherly role - he is the voice of reason in Chapter 9, acting sensibly to hide and protect their belongings from the rain and the potential of men coming to look for them. He also, in the same chapter, prevents Huck from looking at the dead man they find to spare Huck's feelings (we later find out that it is Huck's father). Likewise, as the novel progresses, we see that Jim cares so much for Huck that he often takes Huck's shift at keeping watch at night, allowing Huck to sleep. From Chapter 15 and the trick that Huck plays on Jim, convincing him that they were not separated by the fog, it is clear that Jim feels very deeply for Huck:

"When I got all wore out wid work, en wid de callin' for you, enn went to sleep, my heart wuz mos' broke bekase you wuz los', en I didn' k'yer no' mo' what become er me en de raf'.En when I wake up en fine you back agin, all safe en soun', de tears come, en I could a got down on my knees en kiss yo' foot, I's so thankful."

This love and affection so shames Huck that he says:

It was fifteen minutes before I could work myself up to go and humble myself to a nigger; but I done it, and I warn't every sorry for it afterwards, neither.

This is one example of Huck's maturing as he realises that "niggers" are people too and it is wrong and cruel to play tricks on them.

Thus, I would say that during Huck and Jim's voyage down the river, more and more their relationship develops into a kind of a father-son role as Jim cares for and looks after Huck and Huck becomes more and more aware of his love for Jim and how he is so self-sacrificial.