" -gap on the front door, assume I just get some weatherstripping, concerned that it is not uniform, also does does not latch, so perhap some hanging issue "

Door is not hung plumb, level and square if it will not lock. Needs to be rehung take the entire unit out, only way to fix it.

" -this back does it seems the strike is too far forward and thus we added a super strike plate, a bit noisy and still feels like it is under tension in that turning knob is not smooth "

You bought a door for a 2x4 wall and you have a 2x6 wall. At this point an extended strike plate is your fix, buy one on Amazon. Your fix look like what it is a hack. And again, were door hung plumb, level and square the latch would operate better.

-the sills were just hanging out there perhaps because we lack any trim around doors?, so added a painted white board, it is best?

By design, you can do what you did or leave, either is ok. However again, your fix looks like a hack job.

" minor gap around the door casing, should i just add a floor colored caulk? "

If you want, not truly necessary. And if you decide to caulk the joint, hopefully your caulk skills are better than your carpentry. If not, leave it alone.

With a door, the hinge side jamb has to be perfectly plumb in both directions.

The top of the door has to be 90 degrees to the jamb

The opposing jamb has to be the same distance from top to bittom as the hinge jamb to hold the door right

The door was installed by someone who didn't know what they were doing. You have temporary repairs... the answer is to replace the door and have it done properly.

To start with, when you have to extend the door jamb (door made for 2x4 wall in an opening that's deeper than that), you extend it on the outside to avoid the problems you have with the strike plate.

I'm going to guess this house was flipped. There's new flooring going up to a door that was half-assed when it was installed. Fixing the door right is going to take a lot more effort because you will need to trim back the floor. It's going to be that way with everything on this house.