There is a little lock icon to the left of the password. If you lock that it will keep the password saved. We have talked about the auto-connect feature and we are looking at implementing it for the next release.
God my bain... lol... We have tried MANY things, but we have been trying to figure out the best way to show this information. We have been discussing a new way to manage the ships and their pathing, and hopefully we will have something put together in the near future. Currently you can look at the AI (ships in motion) tab on the ships screen. If you click on a ship you can jump to the destination, or source (in the case of harvester) planet. Not exactly what yu are looking for, but it might help.
Cancelling the AI should stop the ship. I'll look in to this one and get back to you.