Welcome aboard!
I’ve personally never trashed the artifacts- you never know what blueprints you’ll find, and the credit and hydrogen rewards are better when you research them. Depends how large your backlog is, though. Careful storing them on a planet / moon - I discovered that it keeps everything in that system from producing shipments, not just the planet they’re actually on.
No way to PVP, so that other ship was safe! Dock a damaged ship at a planet and it will slowly repair.
At some point the transports will have shipment computers, which will allow them to automatically pick up shipments, but it’s not automated per se.