I think symmetry on both sides of 'And" is important. I'll put two options below.

Homes

For thousands of years, people have used vast amounts of wood for building and heating their homes.

For thousands of years, people have used vast amounts of wood to build and heat their homes.

I would say 'diverse" fits the sentence better. Diversified is the past tense of the verb "to diversify" (like a stock portfolio).

Yes. "I will" has stronger meaning compared to "I'll' which sounds more casual. I'll finish this tonight VS. I will finish this tonight. It comes from the spoken emphasis.

Hiding very quickly under a desk. Imagine diving into water like you do during swimming.

I think it depends on the type of pronoun.Object pronouns (him , her ) sound fine when used with 'according to'. Subject Pronouns "he, she" are incorrect.

"Do I make myself understood?" is something a parent would say to a child, or a boss to his or her young worker. Don't use that one.Try to ask something else like "do you have any questions?".

It’s is a contraction for it is or it has. However, it is not correct in this sentence."It" is the correct word choice for that sentence.

These are just my opinion yadda yadda. 1. Might have vs might had: Might have is not a definite statement, which fits the sentence.The word had would make the cause known and not fit the sentence at all 3. The word out is not necessary, the verb listing is enough. 4. This was an event in the past so 'had' is correct. People have stopped working out of their house means that they still don't work out of their houses in the present because of that fear. Also, for the past week sounds much better than for the past one week.