Gosh, I am so sorry about all this stuff going on in your life. Your poor dad. It makes me want to cry. You certainly don't need to feel embarassed about him. What a hard thing to go through at that age.... so many changes.
I feed my tiels Pretty Bird pellets with some seed mixed in. The also love veggies, some fruit, POPCORN and all sorts of different little tidbits. Yes, they can adjust even if they are older.
I got one of my tiels when she was 12... she is now 22.
She adjusted just fine. I'm sure a larger cage would be welcome... the more room the better for birds. The saying goes... buy a cage as large as you have room for and spend as much as you can afford. For tiels, you probably know, the very tall cages are not appropriate... they need to be more square shaped. A larger cage just has more room for toys and things to keep them occupied and for exercise.
If you change her cage, you might want to introduce her to it slowly... put her in it for a short period of time each day and as she seems more comfy in it, do away with the old one. Put some millet or minced up apple or some other goodies in there so she has a reason to like being in it.
Like I said, one of mine is right around 22 - not exactly sure - but they say they have an average life span up to 20 years in captivity.
Hope this helps and I hope your h's surgery goes well and he heals up more quickly than expected. Take a few deep breaths... don't forget to take a few minutes every day just for YOU.