Grammar

Hello, soon I'm going to take a test and I'd like to know how to complete the following sentences correctly, thanks in advance

1) The president signed a special order ______________ him to stay
a) allowing b) to allowing c) that allowing d) which allowing

For me C and D could be right, but can you explain me why are they using -ing?

(I really don't know how to explain this one, however I do speak English so I know that the one I high-lighted is right. Sorry about not having advice for it though.) 

2) Did you read any of Randy's books? -No, I don't like _______ Randy writes.
a) such b) that c) which d) what

For me the answer is D.

(You are Correct!!!)

3) Will the andersons move when the child comes? -No, they are going to ___________ the house.
a) large b) enlarge c) larger d) make large

For me B is ok, but what's the difference between Enlarge and Make large?

(In English we don't really use make large in any way, if you see "make large" usually it's in a definition however under two conditions you may see "made larger", or "making larger". Made large is really improper or slang in english. Enlarge: is when someone builds on or adds on to something that they already have.) 

Thanks in advance