"My old grandmother"
Translation:Moja stara babcia
It depends on situation, but generally there is nothing rude in it. While speaking in her presence I would probably skip "stara", but it is also fine to say "Moja stara babcia potrzebuje trochę pomocy (genitive)" [My old grandmother needs some help].
I think it's more common and polite to say starsza /but as I have been told those things are regional/personal/ , and this would confuse everybody , older of the two?
Colloquial - no. There are some diminutive or hypocoristic forms, like: "babka", "babunia", "babusia", "babinka", "babuszka" (russicism), maybe also others.