Ah, the gov has been like the boogey man, every time you think that must be it for him, he's back, like Mike Myers or Jason, etc.
So, as it WOULD HAVE been a satisfying scene to SEE him die, and they didn't show it...despite its cathartic power, either the scene didn't come out and they cut it, or, they needed to NOT show it, etc...IE: We see him down, hear a shot, but, really, we don't SEE him shot....HE could have shot someone, one of the woman still loyal to him might have shot his would be killer, the shot was unrelated distracted the shooter giving him time to escape, she could have MISSED, etc. (Lots of alternatives...)
(Granted, stabbed though the heart is normally fatal, if you have one.)
As for the baby, not enough info, but the kids all scattered in the wrong direction when told to get the bus...so, getting the baby would make sense. Blood in the carrier could be from anybody, but all the kids other than the baby seemed accounted for....but if the baby was shot in the carrier, it would probably still be in it unless they have what's left of it, turn, and start craving brains, etc. Granted, a walker might have eaten it whole or something?
Hersh was a goner, but really, I think the gov might have picked Mersh to eff up as she was a real bug up his ass after the whole "you killed my daughter and stabbed out my eye" thing. On the other hand, he would know that Hersh's death would cause the most pain to his foe overall, esp as Hersh gave him the ammo about Hersh's daughter, etc...and gone for whatever would NOT lead to a rational discussion/not a fight....as he clearly wanted a fight.
The tank blowing holes in parts of the compound that would have been useful to not blow holes into, and not blowing holes in the (Not spaced out as they would be better of tactically at least) tightly grouped defenders ranks, along the fence he at least already wrecked anyway, etc....was a bit short sighted, albeit he did not seem like the sharpest knife in the drawer, or was perhaps a really bad shot, etc. That's probably to make sure NO ONE would stay at the prison after all that...and another road trip saga could commence with a mingling of the two remaining parties.
Actually, the shot per hit ratio was pretty bad for both sides. Spray and pray was the order of the day...with ONLY the little girl with a 1:1 kill ratio, at the end to save the pinned down party.