OOp

So I'm trying to learn OOp. I learned about all the features (inheritance, polymorphism and so on). I have two simple questions:

When is it advisable to instantiate objects instead of just using static methods? I always seem to diverge to imperative programming using only very few OOp features.

Don't OOp programs need a lot more of memory and processing power?

Thanks!

I always seem to diverge to imperative programming using only very few OOp features.
What are some problems you've tried to solve with OOP, and how did you end up solving them? Maybe we can suggest more OO solutions.