Do mobsters and those connected believe they are going to heaven if they kill people?

You would have to pose that question to the mobster of your choice. Everybody including mobsters/wiseguys have their own personal beliefs so there is no clear answer to that question. Some are just plain evil and either don't care about God & heaven or actually in rare cases worship the devil; case in point, Mad Sam Destefano who was the worst torturer/murderer in Illinois history. Generally wiseguys consider doing a hit as either family business or as personal and in that case, the person getting hit is usually the worst sob in the world to them. So in either situation a wiseguy likely believes he is doing a good thing for either his crime family or himself. It's looked at as taking care of duty or business. Then there are those few that actually abhor violence so they try not to get involved with the heavy work directly. Those guys usually become some of the biggest drug addicts or alcoholics to come out of the organized crime world. Billy Beattie who was an associate of the Westies in the 70's and 80's is a good example. Beattie began taking drugs and drinking heavily to help him deal with the fact that his organization was committing many murders at that time for the LCN bosses. Eventually it earned him a contract on his head by Jimmy Coonan the Westies boss, which in turn led him to flip and rat out Coonan and many Westies members. This helped to seal their fates at the hands of government prosecutors in the late 80's.