1. Having a jump capable mothership with small scout ships would work, but I always just find it easier to make a jump capable sensor ship and small geosurvey and gravsurvey vessels to come with him. He flys in, checks the system for enemy threats with long range thermal, EM, and active sensors - then returns to the jump point to act as a gateway for the survey vessels to enter.
2. Asteroid mining ships work just like automated mines, except they only function on asteroids. The minerals are placed upon the asteroid itself. You have to create a "colony" there to mine it, but no people will be brought there and you can delete it later. You can either let the minerals build up and haul them off using a cargo ship, or drop off a mass driver and have it send the minerals to a colony in the system (which also needs a mass driver to "catch" the minerals). I don't build mining ships, since I find it easier to just build automated mines and drag them around with my cargo vessels after they've mined a place out.
3. I've tried it, but I've never really had a Sorium shortage to the point that I needed to do it. It works, though.
4. You can colonize anything in your gravity range, which can be adjusted at the start of the game or in SM mode in the race details screen. Go into SM mode (Ctrl-S) then the race details screen (Ctrl-F2) and you can edit the Ideal Gravity and Maximum Deviation numbers under the Environmental Tolerances section. Setting the Maximum Deviation to 1.00 will let you colonize anything from 0 to 2 gravity (which means every single planet or moon in Sol).
The funny thing is, if you make your gravity deviation 1, it's easier to colonize Mars and its two moons than it is to colonize Earth's moon, since Earth's moon is set to a significantly lower base temperature.