1) Are Pompeii and Vesuvius open on Monday?
Yes.
2) If we take the fast train from Rome to Napoli, how do we get to Pompeii from Napoli Centrale.
You need to transfer to the Circumvesuviana line, details here. Get off at Pompei Scavi station.
3) One in Pompeii, how do we get to Vesuvius?
Get back on the train and go to Ercolano station, where there are minibuses to take you up the mountain.
IMHO Pompeii and Vesuvius is too much to attempt in a single day, especially if you're starting so far away. You need most of a day at Pompeii. Vesuvius is better saved for a separate day, and combined with the ruins of Herculaneum.