Kaladin is correct; the game is currently at a
very early stage in development and lacks a lot of features that would make the game playable - but these WILL be added as part of future updates. The invade system order is simply one of the features that hasn't been implemented
yet but will be coming in future.
As Kaladin said, the game lacks an AI (Artificial Intelligence). The AI is basically what controls the other empires and minor races, but it will also have a number of other uses, such as controlling the system governors that will decide what to build in systems that you tell the game to automate production in. As there is no AI to control the other races and empires, they quite literally sit there and do nothing because they don't know *how* to do anything - not even feed themselves.
This most certainly isn't a bug, it's simply a case that it hasn't been built yet, but it will. The AI will likely be the most difficult-to-program part of the game, and as such it's going to need a lot of development time; we've looking at implementing a very basic AI in the game within a years time. Obviously we can't see the future though; it make take less time than this, then again we may encounter problems or delays. But an AI will be implemented in the game eventually, and once it does, we'll all be able to play a proper game.

The KNOWN ISSUES IN THE CURRENT VERSION OF SUPREMACY thread in the
Supremacy Bug Reports forum contains answers to many of the issues like you just mentioned. It actually already explains about the AI, but it didn't contain a section on the troop transports. I've now ammended it to explain this. Please take the time to read the thread, and check it out whenever it is listed as being updated because it is a locked topic - it will therefore only show up as having "new" posts if it has actually been updated to contain new or updated information.
Oh, and welcome to the forums, rjoseph70.

_________________"Anyone without a sense of humour is truly at the mercy of the rest of us."

