No, you cannot! You either love something or you don't. There are no degrees of love. It's black and white. It's like "delicious". It always amuses me when somebody says the meal was "very delicious". Unfortunately, that's just bad English. The meal was either delicious or it wasn't. If you want to use "very much" then you should use the verb "like", which can have various degrees.

It is grammatically correct, and you can use them together.

If love is an emotional, or is referring to self-expression then it is subjective, so you can have degrees of love if you so desired, just as you can have degrees of like.

James is correct, but note that plenty of native English speakers DO use them together, all the time, every day.