Well, 'divers' is an old-fashioned word, I think, and according to my dictionary they are different. Or rather, 'diverse' is 'different', while 'divers' is just 'several'.

I'm not sure that I understand your concern, but questions do indeed take ' do ' unless the verb is the copula, ' be ', or who/what/where/when/why/how is the subject.

#2 is not a natural formation, either a or b.

Turn the next corner and go a short distance.

You can, but native speakers normally use simple present in the subordinate clause: I'll do what I'm asked to do.

F: I've just baked some muffins. M: Now I understand where this good smell is coming from. F: It's almost tea time. Would you like a muffin with tea? M: I'm home. I'm e xhausted, and I want to take a long bath. F: You must be tired. I'll run your

No. 'I' should always be capitalized. The sentence is otherwise acceptable in informal situations.

Not likely. 'All the sugar'; 'All belief'. But I suppose 'all the cow is edible' is possible.

Yes, a preposition, too. I knew there was something I had forgotten.

Check all the items in each room to compile a correct inventory list / Check all the items room by room to compile a correct inventory list.