Pavane, re not singing songs about mortality in nursing homes, I refer you (with tongue firmly in cheek) to this thread:
Songs NOT to sing in nursing homes

; D

Seriously, though, when I first started doing "old folks" gigs, a rather young activity director gently scolded me for singing "On Top Of Old Smoky" -- a song which is very popular among US elder folks, by the way -- because of the verses that say a false-hearted lover will lead you to your grave and then the grave will decay you ... .   I discovered soon thereafter that it's not the elderly who are bothered by references to death. They're more realistic about, and generally more accepting of, the mortality of the body than younger generations. You don't want to be morbid, but I don't think you need to go out of your way to avoid songs that refer to death.

What I DO avoid is songs like "Maids, When You're Young, Never Wed An Old Man" or "I Don't Look Good Naked Any More" -- songs that take the obvious fact that we get less attractive as we age and rub it in.    E.g., I will not sing the line "Nobody wants you when you're old and gray" - in the song "There'll Be Some Changes Made" - at a retirement home. That's just too insulting.   On the other hand, songs like The Weavers' "Get Up and Go" and Steve (?) Walters's "The Memory Song" or the parody "(I Can't Recall What Was) The Last Thing On My Mind" go over very well -- especially if the performer is also not a spring chicken.