failures
I was taught that there are 4 types failures:
1)fail to fire, 2)fail feed, 3)fail to extract, and 4) fail to eject. I read and hear the term "double feed" now and then, but am not really sure if that is technically valid and not exactly sure what one would look like.
To me, from your pics, 888 shows a fail to either extract or eject, if in fact that is a spent case wedged in the ejection port. If you are consistently getting spent brass stuck in the pistol, what follows does not apply. Rather than drag out my response, I will proceed on the belief that both pics display fail to feed.
If that is a live round top most, pic 888 is a fail to feed. Pic 999 is a fail to feed for certain. Fail to feeds can often be traced to bad mags, as others have noted. Factory mags for my HP all have a "mousetrap" spring on the rear. I cannot say if the touted Mec Gars have same, or if MecGar and factory are indeed the same thing. May well be.
Assuming you are running fresh, quality factory ammo( I would use FMJ as a default) and your pistol AND MAGS are clean and lubed, , I would try new, quality mags next.
As others have noted, ammo, mags, and I would add, fail to maintain and lube (dirty gun) are the most common causes. The HP has reputation as reliable due to the relatively straight path of the upcoming live round into the chamber. Hope yours gets to running right soon.