A decision problem is any problem that the answer to it is either yes or no.
According to xlinux.nist.gov website, a decision problem to be decidable may be completed in a finite number of steps by an algorithm that halts on all inputs.
P P is problems to be solved in polynomial time. NP is a problems to be solved by a Non-deterministic turing Machine in Polynomial time, and it is called "Non-deterministic Polynomial Time". Source
According to MIT News, it means that if any solution to any problem, can be viewed in polynomial time, then it can be viewed in that time.
Their are seven questions, that if anyone answer it, they get a million dollar Source