Welcome to the forum.
First of all, be sure to patch up (to 1.91) and download the TDM AIs instead of the defaults.
1 and 4: The AI’s suck at trade and can be easily exploited. If you want a challenge from singleplayer you should adopt a no trade house rule. Population you can get from capturing planets (with troops) or capturing colonizers or pop. transports (with Boarding parties or Intel).
2: That’s the way the game works. However, except from the first few turns, expect the AI’s (TDMs at least) to put quite heavy defences on their HWs.
3: Point Defence (PDC) makes missiles obsolete soon enough, so don’t expect your über weapon to Last very long
