1) You can build colony modules on tiny ships for only 38 manufacturing cost.
Yep you can. It's extremely slow-moving and has no range, but it can be done. I am personally quite fond of a cargo ship with two range extenders, one drive and a colonizer. Usually all you need.
2) You can build ~12 sensors on a cargo ship from turn 1 and reveal most of a medium galaxy
Yep you can. It costs a ton of money though, so you need to decide if it's worth it. I generally prefer to research the first thing in the engineering tree to get the first upgrade for sensors and drives, then construct my Visionary sensor ship. It'll take you a few turns to research and then build the ship, but you get a MUCH better one than the turn one model, and it doesn't cost you 2500c.
3) You can build ships that have more mass on them than is allowed
This issue is more around you designed a ship in a previous game which used X hardware and took up Y mass. In your new game you have researched X hardware, and the ship becomes available to construct, even though you don't have enough miniaturization technology to achieve the required mass of Y. This is a known bug.
