Question 1) This is actually a coin flip theory question. If villain is shoving literally any two cards then you call with anything that has a 51% edge against those hands. However, if the amount you are risking is a large % of your BR then you would be a fool to go so thin. Its really risk/reward question that is hard to answer without knowing your BR.

Question 2) This is most certainly ok if villain is being a lag. Don't focus on whether opponents are tilted or not. Focus on what tilting does to their range of hands and how they are acting to you.