having hard time finding the following language laws

Hello there! I hope somebody can give me a hint on where to look up the follwoing language law.

I brought a sweater with me (1) to keep warm, (2) for keeping warm.

I know only intuitively that the first answer is correct, but still cannot see much difference between two of the options. If you know what is that, could you please give some explanation?

Another langugae law that I barely understand is the following:

Those boys climbed up the … tower last night.

(1) church’s (2) church.

I could not find any language law pertaind to this situation. I am somewhat confused. To me, both answers are possible. But it seems that it is not the case.

I brought a sweater with me (1) to keep (myself) warm, (2) for the purpose of keeping myself warm.

Those boys climbed up the … tower last night.

(1) church’s (2) church. (‘Church tower’ - which also means the tower of the church - is standard as we usually do not make a possessive form by apostrophizing the name of a building.)

In the English test, it is stated that the correct answers are:

  • to keep warm
  • church’s tower

I didn’t say they are incorrect. I only indicated my preference or the usual usage. See these examples: school bus, family members etc. As regards ‘keep warm’, the words ‘with me’ would suggest that it is for your own use. So, it can convey the idea.

Do you mean that both options possible?
[/quote]

Yes, because they unambiguously convey the intended idea, but I do not prefer the original.