This should work very well from my point of view....

https://www.tp-link.com/us...

Yes, you can, just flash OpenWRT (https://openwrt.org/toh...).

To set up something like you want, you need a NAS, file server, media server (e.g. Raspberry Pi) which you install in your network.
This way you can access your files without internet (all devices have to be in the same network).

Or simply get an external hard drive (USB stick) because you probably don't always want to take a NAS + cable and router with you ;)

Unfortunately, you misunderstood the USB port for connecting an LTE stick.
This means you can get internet through it (subscription + LTE stick necessary, of course).