Do I need to have this thread screwed all the way in on bottom bracket BB-UN53
As long as the BB is being held in place properly the stick-out of the cup shouldn't be an issue. Make sure the BB can't move from side to side when putting axial force on it.
Also make sure the crank arm on the side of the cup that sticks out isn't rubbing against the cup. As long as those conditions are met you should be fine. 

The forces on the bottom bracket in axial direction will be quite low under normal use conditions so I'm pretty sure the plastic cup will work fine but if you want to play it safe use the metal cup since the threads won't strip nearly as easily as on the plastic cup, also the tool-interface (the grooves that the tightening tool falls into for tightening the cup) can more easily be damaged on the plastic cups (I've had cases where they have become very stuck in the frame). 

Do make sure to apply some sort of grease or anti-seize product on the threads especially on an aluminum frame to prevent the metal cup from seizing. They can be very difficult to remove in some cases

I have seen bikes which have spacers/rings in between the non-adjustable cup of the BB and the frame, similar to this: 

You could consider using such spacers to properly center the BB in the frame. Do keep in mind this may mess with your chain alignment a bit. The difference should be so little though that it shouldn't cause issues. if you find that it does cause issues you could potentially solve it by using a BB with shorter or longer axle length.