Can a person with a felon get a law license or become probation officer,paralegal?

One can be denied a license to practice law upon a finding of "moral turpitude", so it's possible but not likely.

If parole officers are licensed in your state, denial of a license is likely on the same basis.

Are paralegals licensed in your state? Why?

Parole officers have to be licensed with what they call POST in the US, and they all carry guns, so a felon can not do this.

Paralegals are not licensed in many states, since for many they are considered a highly trained clerical worker, nothing more, they can not give legal advice, just do legal paper work.
Legally they can not give legal advice anywhere in the US.

You will not know if they will accept you as an attorney till you go to law school, pass the bar test and apply to practice law, then that states board will decide.

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You will not know if they will accept you as an attorney till you go to law school, pass the bar test and apply to practice law, then that states board will decide.

Well, correct, but in the wrong order. One applies and then takes the bar exam.