1. I think the game just want to keep X number of explorers just because of it. They're *mostly* use less at later stages of the game, unless you want to scout out enemy systems before you attack. Then again, in late game, you should have no problem affording a bunch of explorers. They're pretty cheap.
2. There are two "load troops" order, "load at nearest", and "load at specific colony". I think you want to use the latter (select the fleet, right click / ctrl-right click on the colony, and say load troop.) Otherwise, "nearest" is probably determined by the lead ship of the fleet, which could be stranded somewhere on the othersie of the galaxy.
3. The construction ships do work on automated. Maybe you already have lots of resources? They might not build anymore if you already have lots of resources and there is no demand for them. The expansion planner will list all your resources and how much demands there are for them.
4. Yes, those are resources you have sold but they have not yet picked up. I have no idea what happen to them when you go to war, but I know they will shoot at the enemy's cargo ships when they try to dock.