2. "How do you think we should deal with this?" This is also correct. You may also use "could" but the meaning is slightly different, although in many situations they would be completely equivalent. When you use "should" here, you are more direct, you have the obligation to handle the problem.
3. "That can be possible." This is also correct in my opinion. Although you will see many posters disagree with me in this point. Usually "can" should be reserved only for ability and "may" or "could" for possibility, however, I have seen many uses of "can" with the meaning of possibility too. It is also correct, and maybe better, to say "That could be possible."
4. "Let me know what time should suit you best." This is correct. You could also use "would."
Remember that usually "can" is reserved for "ability." See for instance: http://www.usingenglish.com/forum/as...can-could.html
I also recommend reading the related thread: http://www.usingenglish.com/forum/ge...dal-verbs.html
This last one is particularly interesting because it is about a book whose main goal is not language itself.
Not a native speaker