Yes, you can.
Can u install keeping your stock trigger itself in place for those who don't like travel screws on triggers???
No on the 2nd question. The Match Trigger Kit does not change your reset. The stop screw minimizes your over-travel thus, in a way, offers you a shorter reset. If you want to mechanically shorten the reset, I'd recommend the GrayGuns SRS Kit. It does an incredible job on shortening your reset but does not cost you an arm and a leg.
If you are going to go to the trouble to install the match trigger kit then put in the trigger with the set screw. If you ever to go to sell to then it is complete and someone can at least see the trigger with the set screw even if you do not screw it out for it's intended use.
HK - No Compromise