In Present continuous^x, Gerunds^x, Difference between^x

Hi, everybody I have a few questions. What's the difference between: gerund, past participle, present continuous and present progressive? Can you make me an example of each? How do I recognize them?, to what question do they answer?

1) Do May / Might NOT (like CANNOT) express an interdiction = must not ? ex: ? CJ

Thank you very much, CJ, for your answers! Some more questions if you wouldn't mind: 1) Do May / Might NOT (like CANNOT) express an interdiction = must not ? ex: ? 2) Mrs James is in hospital and HASN’T BEEN ALLOWED TO have (and NOT “could have”) a cigarette after her meals. (correct ?) 3)...