Realistically, most self-hosted services will work "offline" (no internet connection), provided you also power a local network during the outage as you will have to access it somehow.
This also plays into the other factors, as self-produced power is usually far less than what you'd get from the grid (I.e. you'll probably want to avoid things like heavy transcoding).
That's unfortunately not true. There's nothing inherently wrong with using older speakers, but check that they actually work correctly and are still technically sound:
the driver coils sometimes burn out, meaning that particular one stops working
the driver diaphragm might tear (rare), or the suspension might tear (more common than the other). The suspension rings are especially vulnerable if they're made from foam, which was widely used in older and/or cheaper models.
cables or welds might corrode/break/tear internally or at the terminals, meaning drivers or the whole speakers no longer work.
The drivers are usually the parts with the biggest damage potential, as they actually contain moving parts. But as long as everything is still working fine, there's usually no need to replace the speakers.