Newguest1. Everything that happened was my fault. Can I also say: Everything what/which happened was my fault.
2. The last time (that) I saw her, she looked fine. Is the word "that" the object of this sentence so we can omit it?
3. Martin tried on three jackets, which didn't fit him. Can I also write:..that didn't fit him. Do you think it is a non-restricitive relative clause?
4. Two men, I had never seen before, came into the office. Is it also OK to write: Two man, whom/who/th
1 - I don't think you can use "what", and for some reason I don't like "which". Also, I think that "everything" should be written separately, "every thing".
2 - You can leave it out. I don't know if it's used as a relative pronoun or a conjunction, though.
3 - With the comma "which" is ok, but not "that". If you use "that" without the comma, you get a restrictive relative clause that refers to the jackets and specifies what kinds of jackets those were: jackets that didn't fit him.
4 - If you use the commas you need to add "who". With no commas you can leave it out.

EDIT: I hadn't seen CB's post. I just read it and I think I don't agree on this:
3. The sentence is fine with that provided you leave out the comma and Martin tried on at least four jackets in all. If you use a comma, only which is possible and in that case Martin tried on a total of three jackets, none of which fitted him.
4. Your sentence with commas is wrong. If only two men came into the office and you had seen neither one before, write:
Two men, who/whom I had never seen before, came into the office.
If more than two men came and you hadn't seen two of them before, write:
Two men [who/whom/that] I had never seen before came into the office
I don't think the number of jackets or men is important when considering relative clauses. 