Yes, it's correct. Your grammar is correct and your meaning would be well conveyed. But It would be more natural if you add some changes like below. xx 씨랑 편하게 얘기할 수 있으려면 많이 공부해야겠어요. 1) 할 수가 -> 할 수 2) 해야 해요 -> 해야겠어요. It could be translated as "It seems like I need to study hard to make the conversation fluently with xx." I think native Korean speakers usually prefer to express their opinion in an indirect way rather than in a direct way. So, for me, '해야 겠어요' sounds more natural in this situation. I hope this comment could help you, and please leave comments for different opinions.

Yes, I think you got it correct. 편하게's original meaning is comfortably or conveniently, but it can also mean "without difficulties or hindrance", which I think is the meaning in your example. You can think of it as "not giving yourself or the other person stress".