Every 82-yr-old is different. My dad had dementia and spent his last 2 years in a nursing home; he passed before his 82nd birthday. My mom is late 80s, healthy and still going strong -- full mental capacity, lives independently, follows a fairly "typical" schedule each day, etc. She may be slower than she was 30 years ago, but she's definitely nothing like the condition my father was in. My dad never would have been able to handle such a trip. My mom would simply need an
ECV or wheelchair to help her get around, though she doesn't use one regularly; she might prefer scheduling quiet non-park days as well. So each individual is different even at the "elderly" age range.
I’m having lots of concerns about going with him , such as mobility, too much excitement (I’ve heard sometime it’s too much for elderly and causes health issues) , what if I need a doctor, can he tolerate such long days in the park...and many more.
Mobility -- he can certainly do the parks in a wheelchair. DLR has more older attractions that aren't as easily accessible, but he will receive a "wheelchair return time" if the queue isn't open to his wheelchair. That shouldn't be a significant concern. I suggest asking on the DLR Forum about which attractions can accommodate his chair without need to transfer, since that sounds like possibly the hardest aspect for him.
Too much excitement -- I'm not sure what this means exactly, especially as related to an elderly person. Maybe help him prepare by sharing YouTube videos. Get the grandkids to watch with him, either via online chat or phone, so he (and they) are familiar with what to expect. If you feel the trip may be more than he can handle (excitement or otherwise) it may be best to plan something more local or low-key for him. If there isn't a lot of contact already, maybe try to do some video chats or speaker-phone calls with him and your kids, so they can all visit a bit and be somewhat used to each other before the big trip.
Causes health issues -- well, I think that largely depends on the individual's personal health. Unless there are other specific concerns (heart problems, diabetes, etc.) I don't believe a Disney trip will "cause" health issues. I suggest he (or someone who may be caring for him now) speak with his current physician about the trip and any concerns. Stay hydrated, eat properly, try to stick to a somewhat normal schedule (awake, meals, bedtime, etc.) and get plenty of sleep.
If he needs a doctor -- what will you do if one of your kids gets sick or hurt and needs medical attention? Same for dad. There are local clinics and hospitals in the area, and pharmacies for meds. Bring your/his insurance info if it covers international travel, or have a credit card that can handle a medical bill if you/he either doesn't have coverage or the coverage requires pay-up-front for reimbursement later.
Can he tolerate such long days -- this is going to be very subjective and based on his personal needs. How does he feel about long days? Does he manage a fairly typical day at home? Or does he require a lot of extra time to get started in the morning and retires early evening after dinner? Does he get out and about at home -- to the stores, church, park, zoo, anything like that? If he's been housebound, you probably have a real concern and I would think twice about the trip. But if he's able to manage a day out at home, he should be ok at Disney. I do recommend trying to stick to a somewhat normal schedule though, making sure everyone gets plenty of sleep. If you have a late night, follow it with a morning in the hotel. Don't try to do early mornings and late nights on the same day.
Do you have other specific concerns regarding his health? You haven't mentioned that he has cognitive challenges, which might have greater impact than his partial paralysis. I would get him or his caregiver to discuss the trip with his medical provider. Maybe they can conference you in during the visit so you can share your concerns or hear the doctor's advice.
Enjoy your vacation!