Yes, you can use it fully offline.
To back it up I believe you'd just need to backup your .pass and .gnupg directories.
I haven't used keepass, but the entry from the archwiki should give you a good idea of usage, and it also lists some helper apps: https://wiki.archlinux.org/title/Pass
In the US, many public universities allow access to the public, including use of computer terminals that will allow access to paid databases. In many cases, you could bring in a usb stick and save copies of articles downloaded from such databases, or at worst you could pay a small fee to print some stuff out. AFAIK, that kind of access varies state by state though, so you need to call university libraries near you to find out.
I'm a college professor in the humanities (religious studies, history). Got into linux about 5 years back, partly because it comports better with my lefty politics than the alternatives, but also just because I've long been a closet computer nerd. I currently run a couple of proxmox servers on old optiplexes I grabbed off ebay. Full *arr stack with jellyfin on docker, a Tails VM for TOR stuff, NAS (omv on a vm), some other dockerized stuff: linkding, radicale, alexandrite (a self-hosted lemmy client, which I'm currently writing this on), various backup utilities.
It's basically just a hobby for me, though the switch to linux has also totally changed my academic workflow, e.g. I do all my writing in nvim + latex now, use syncthing to sync my home desktop, laptops, and office computer, etc. I dig divesting myself from corporate computing to the greatest extent possible, appreciate the privacy benefits, and generally just enjoy the community-driven spirit of the whole thing.
I mostly use debian + docker or alpine + docker for this kind of thing (usually running as VMs on a proxmox server). Both are utterly reliable in my experience, though I've been tending more often toward alpine these days, because it's just so light and simple. I haven't tried any of the immutable systems, in the general spirit of why fix what's not broken. I don't even bother with snapshotting either, though that's mostly because I use some of the proxmox tools for backing up the VMs.
I love linkding, couldn't live without it.
Yep, I've got a stack of 5-10 year old optiplexes (optiplexi?) running proxmox.