If you're talking in general, it's more common to use -ing, but you can use the infinitive as well. If you're referring to a particular occasion, it's more common to use the infinitive. The same is true with "prefer" and other verbs: 1) "I love traveling ("traveLLing" on my side of the ocean). What about you?" "I prefer playing chess". 2) "I'd love to travel next summer, I haven't done it for years. What about you?" "I'd prefer to spend my vacation ("holidays" on my side of the ocean) at home. However, this is a subtlety, the difference is not very important.

Both are fine. "I love to pet my dog" and "I love petting my dog" are both correct and mean the same thing.

Both work. You can say "I love to fish." or "I love fishing." You can even say "I love to go fishing." All three of those are correct and common English. :)

Both