I'm an advanced diver with over 250 dives, so I'd be happy to help you in whatever way I can.
I'm not medically qualified to tell you if your health issues would affect your ability to dive. What I would suggest is to start reading the PADI website: http://www.padi.com/scuba/
There's a plethora of information on there about how to get certified. You'll need to get a certification card from one of the dive agencies, and while opinions differ about which agency to use, PADI is the most prevalent, and a PADI cert card is accepted all over the world.
Here's a good place to start: http://www.padi.com/scuba/scuba-divi...q/default.aspx
As for your health issues, here's what PADI says:
About Physical Challenges: Any individual who can meet the performance requirements of the course qualifies for certification. There are many adaptive techniques that allow individuals with physical challenges to meet these requirements. Individuals with paraplegia, amputations and other challenges commonly earn the PADI Open Water Diver certification. Even individuals with more significant physical challenges participate in diving. Talk to your PADI Instructor at your local PADI Dive Shop or Resort for more information.
You would likely need to get a medical evaluation and be cleared by a doctor to get certified.
When you say "the mask they provide"...I personally wouldn't use a rental mask, or one of the PG's snorkeling masks, for diving. I'm sure they're fine for snorkeling, but you do NOT want a mask that doesn't fit your face perfectly when you get down to 60 ft., or you'll be dealing with annoying flooding for the whole dive. Buy yourself a decent dive mask from a dive shop. Besides, most places where you would go to get certified will expect you to provide your own mask and snorkel anyway. You can rent the rest.
I wear glasses/contacts, and I don't use a prescription mask - I wear my contacts underwater. Many divers do. (Forget glasses - they won't fit under the mask.) Some divers prefer prescription masks, but I want to be able to see with my mask off too.
So I wear contacts. I do have little stick-on magnifiers on my mask so I can look at the little stuff, tho. (These old eyes don't focus as well as they used to!) You will learn how to deal with a flooded mask, and you will even need to perform a skill in training in which you remove your mask underwater, replace it, and clear it. As long as you keep your eyes closed you won't lose your contacts. I never have.
The PADI website can help you find a local dive operator where you can get certified. We went to Sport Chalet for our initial certifications. Certification requires some classroom work, some time in the pool, and two instructor-led dives in open body of water. You will do your initial dives in the pool, but to complete your cert you will need to do two open-water dives (in the ocean, a lake, a quarry or some other open body of water) with an instructor. Your local dive op can tell you where they take their students.
I don't know where you're located, but if you're not near a body of water, you can do the classroom and pool work at a Sport Chalet or some other local dive shop, and then do your two open-water dives somewhere else.
The PG does offer scuba classes, but I would NOT use your vacation time in FP getting certified! Do it at home. If you're not near a body of water, you can at least do the classroom/pool work close to home, then do the two required open-water dives on the PG.
Another, less daunting option is to do the "Discover Scuba" class onboard the PG. That's not a complete certification - it's really just a "taste" of scuba. They'll give you some basic training onboard the ship, a little time in the pool to learn how to clear your ears and mask, and then take you on a couple of beginner dives. But if you're really serious about diving, I wouldn't waste my time with that. First of all you'll be spending all that classroom/pool training time when you could be enjoying your vacation. Second, your options for diving are limited - you can only do the few beginner dives offered by the ship. My recommendation is to get certified in advance, and then you can sign up for ANY of the dives...and enjoy them!
Hope this helps! Ask away - I'll answer what I can.