The colony type only matters to the AI (ministers), it has different building plans for each type.
The planet maximum populations increased, or the planet's actual population increased? The only way I know to increase maximum population is to use Atmosphere Converters, but populations (the first number) will increase until the max is reached (the second number).
The movement system works on squares moved. Normally engines give one movement point (one square of movement) each, plus bonuses. Ion Engines have no bonus, Contra-T Engines have a bonus of 1, for all combined (ie. 1 = 2MP, 2 = 3MP, 3 = 4MP, etc), Jacketed Photon have bonus of 2, Quantum have bonus of 3. Solar Sails have a bonus for each level, I = 1, II = 2, III = 3.
Best place to look would be here. Just run a search on whatever nuance you're looking for and there's probably a post dealing with it. Both the Tutorial and the Manual are exceptionally vague. There have been a few attempts to make a fan-made manual (including one by myself), but real life intervened each time
