Kind of. I might say, "It was really nice talking with you after all this time. We should (must is more formal) do it more often." If you say "to talk..." you might want to use the preposition "to," otherwise the word "speak" goes with the preposition "with" ("to speak with" or "to talk to"). Also, you can use the gerund with the preposition "with" ("talking with you"). These are very minor things that might out you as a non-native speaker, but otherwise very understandable.

It is grammatically correct. I think "we should do it more often" is more natural. "We must do it" sounds much more emphatic.

It is correct.