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.
You say this machine is headless. Is it at a remote location? If not, is it feasible to connect it to a monitor an keyboard for a few minutes? If so then you could logout, switch DE, and then log back in. That would hopefully set the DE you prefer as user default.
If that's not possible, then some of the solutions discussed here might be applicable.
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 work for a large state university and run linux on my office machine, despite the fact the IT office dept doesn't officially support it. I told our IT guy once what I'm doing and his response was, "cool." Of course I'm totally on my own if anything goes wrong. It helps that I'm a prof and most of my on-campus work doesn't involve much time on a computer, aside from basic web and documents stuff. tldr, in my case I'm able to just do it without asking anyone's permission, and it's worked out great for several years now, but a lot of jobs aren't like that obviously.
I love linkding, couldn't live without it.
I've used herbstluftwm on my main desktop for years. Love it. Manual tiling works well for me. Totally flexible and customizable. Switch between floating and tiling with a keypress, etc.
And then on various other machines.
You have to enable it, but once you do it can do them automatically.
Linux Mint Debian Edition. Very windows-like + automatic updates = ideal for people who don't really want to have to learn anything new (assuming your parents are like mine in that respect).
But isn't that every linux forum?