Can someone be sued for having a cheaper app that has the same idea as my app, which is more expensive?

no. you can't patent an idea, only the mechanism that makes it work

Depends.
If their app does the same thing, but does it with different code, then out are out of luck.

No, but you cant use their appname (assuming they had it first) or any of the images or icons etc.

no

only for copyright not for price

Probably not.

Can you sue? Sure, you do not have to prove anything to sue. Can you win? Depends on the details of the case. If your only complaint is that they made an application that does the same thing as your application and they sell it for less money you have no case. You could have a case if you could prove they stole the idea from you and that they were not filling a common need.