Beretta 92a1 cycling issues?

honestly it sounds like you are holding the slide release down on accident 

Limp wrist?  Check how you grip the gun through the whole motion of the fire and recoil.  Sometimes, particularly with the older school metal frame 9mm's like the beretta 92 or the CZ 75, if the shooter's grip is not firm enough, to much of the recoil momentum to be taken up by the wrist, rather than contributing to the full motion of the slide and the action won't cycle completely.  It also happens when people flinch and anticipate the recoil.

A lighter spring my help your symptoms, but may also be harder on the gun if it is so light the slide slams back too hard or doesn't bring the gun back into battery.Also make sure the slide rails sufficiently lubed.

Beretta 92?........usually do not have cycling issues with in spec ammo.

I would suspect the ammo as the issue there-period.

On the slide not locking back after last round-I would look at the magazine to make sure the lip on the follower is contacting the "lifting lug"  (my terminology) on the inside of the slide lock/release. Or possibly the spring on that slide lock is missing or out of place.

Really hard to diagnose all of your issues. You say factory ammo cycles fine but reloads do not. Looking at that from our side says there`s a problem with the reloads...not necessarily with the powder loads but what changes were made in the case dimensions upon firing.

 I have seen cannelures in the wrong place cause stovepiping even in virgin factory ammo. That groove around the case is obviously smaller in diameter than the case diameter at that point. If that cannelure diameter happens to be located at the front lip of the magazine when fully loaded it can cause the round to flip up just enough to catch the slide and interfere with the ejection and stop the slide with either the spent case or often the unfired round.

 Also, your own cases that you fired in your gun should resize without problems but cases fired in another gun may cause problems. 

There`s often more issues other than sizing spent cases than seen with the unaided eye. The factory loads fired for the first time will have tool marks in the chamber transferred to the case. After many rounds the brass will eventually wear the steel to a smoother surface and problems ejecting will fade away. Tool marks in a chamber act like tiny fingerprints as far as the grip on the case.  I would advise anyone to not do anything to void a warranty, but, myself that has never made a warranty claim and never plan to...I would polish the chamber. That`s just me and my philosophy to do my own repairs. Once a firearm is in my hands...it`s mine until either traded or sold. Before jumping to conclusions always try different magazines and vary the number of rounds loaded especially in the higher than 10 capacity in a handgun. 

Sounds like it needs a real good cleaning and refit of parts if it's NEW just might be a little tight...