Hey LeadFingers, welcome to the forums!
Kev is correct about building the Outposts; you need Construction ships to build them now. Transports are for invading systems with.
I've just sent an update to Mike, which, amongst other things, includes a new upgrade path system for the Outposts. I haven't updated the Starbases yet as I want to make sure the system actually works. Mike hasn't read the PM yet and it will likely be a few weeks before he can implement it on the update server though.
As for redeploying, Kev is also right about that. There is a redeploy button at the bottom of the screen. Click it, and you'll see all of the ships in the system in a BOTF-style redeploy screen. It even works in the same way; double-click a ship to add or remove it from a fleet. The screen has one important addition though; from this screen, you can rename ships! Just single-click a ship on the screen, and it will show up in a larger box. Click on its' name and you can enter anything you want as its' name.
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As for buying buildings, you can't do that. We will eventually implement a system where you can increase the build rate by paying the workers to do doubl;e-shifts, but instant-build will NOT be in the game. This particular idea has been discussed on the forums for four years now, and the eventual decision was that people didn't want instant-build in the game.
Let us know if you have any other questions.
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