Q1 - In my opinion, in North America, "it's a pity that" and "it's a shame that" are roughly equivalent for minor misfortunes such as "it's a pity/shame that the concert was sold out." However, for more serious problems, I would only use "it's a shame that." For example, "it's a shame that your brother died young." Of course, there are individual and regional varations in English. Q2 - The example sentence is grammatically incorrect. There is a "comma splice" after "...have a good talk." This is an error because two main clauses can't be joined by a comma. To fix the sentence, you can separate the clauses with a period (full stop) after "...have a good talk," or better yet, you can join the clauses with the conjunction "because" to create "... have a good talk, because good communication is ..."

In response to your first question, you can definitely use both phrases as they both express a similar feeling. With regard to the second question, it is gramatically correct in its current form. However, it would also be correct to replace the first comma with a full stop. Personally, I think it sounds better if the first comma is replaced by a full stop. Example: It is suggested that you two sit down together and have a good talk. Communication, after all, is the solution to the problem.