Really depends on the situation... like how long were they together, and why did they break up, or how old are you, and what sort of contact it is.
If your mother was with him for a long time, and he helped to raise you, then it would make sense for the two of you to be in contact, since you and him might have a "father-daughter" type of relationship, which shouldn't end just because he is no longer with your mother. And in most cases (unless it was a really horrible break up - your mom should be ok with this).
Other than that, in general if you feel that you have to hide the fact that you are still in contact from her, I'd really want to examine why that is. In any case though, you should let her know.
Unless you want lifelong problems, tell your mother. If that doesn't end this unhealthy relationship, you are probably facing a lifetime of brokenness. If you are not of legal age, avoid him like the plague. Call the cops, if necessary. I urge you NOT to encourage him.
No, I smell trouble ahead for you and your mom. Tell your mom immediately and become her ally. She will protect you. Always talk to your mom. You don't say how old you are but I think still an adolescent. You are too young for this relationship. Run fast the other way!
Well, it depends in the situation. Is he a pervert? My mom broke up with her boyfriend, but we still talked. He's like a dad to me. But my moms knows I talk to him and he comes over to our house sometimes.