Conditional or not?

Hi,
Please tell me if my assumptions are correct.
1, They began asking us several months ago if we would stay. -- looks to be a type 1 conditional like "They began asking us several months ago if we could stay."
2. I said I would stay if I could do two shows a night.-- looks to be a type 2 conditional (unreal)
3. If there would be a church in this neighborhood, it would be ideal. -- looks to be a type 2 conditional (unreal)
4. If there were a Burnham wood in ***, they probably would have shipped it. -- looks to be a type 2 conditional (unreal)
But, this doesn't look to be any type of condtional. Or could it be a type 1 conditional?
Would you pass me the paper if you have an extra one?
So, is it the fact that if you have an if-clause and a clause that comes after it, it is a conditional sentence, whether in question form or sentence(?) form?   

1, They began asking us several months ago if we would stay.  Not a conditional at all.  if/whether we would stay is an indirect question.
2. I said I would stay if I could do two shows a night.-- looks to be a type 2 conditional (unreal)  Yes.  Type 2.
3. If there would be a church in this neighborhood, it would be ideal. -- looks to be a type 2 conditional (unreal)  If there were a church ... Type 2.
4. If there were a Burnham wood in ***, they probably would have shipped it. -- looks to be a type 2 conditional (unreal)  Mixed conditional. 2 and 3.

CJ