Assets

If I have ships and items in a player-owned structure, and the owner locks me out because s/he doesn’t like me anymore, what happens to the ships and items I can’t retrieve? Is this an ‘asset safety’ situation, where I will eventually get them back?

Also, can this happen if I’m in a station, and can I assume that all stations are npc-owned?

Stations are npc owned. Unless you have a corp hangar, your stuff should be safe.

As far as items in structure, you can see if you can asset safety them, or see if its a structure push x or one of the frog services can go to, to retrieve your stuff

Asset safety can be manually triggered by right clicking the station name in your personal assets and sending everything in it to asset safety. If the structure explodes, asset safety is triggered automatically, unless the structure is abandoned (has been in a low-power, unfueled state for more than a week) in which case your stuff drops as loot. As Geo said, if it’s a public structure but you’ve been explicitly banned from it you can maybe find another player (or your alt) to move the stuff out of it without having to deal with asset safety.

Stations (the square icons) are NPC owned and will always allow you to dock unless you’re in faction warfare and the system is in the warzone and controlled by the opposing faction.