I would argue that Federation technology
should have advanced more as a result of reverse-engineering alien technology than it did in the previous shows and films. Prior Trek was too restricted by the producers' desire to maintain the status quo; the new movies are freed from that artificial constraint, since the goal is the opposite. If anything, this version is more plausible than having a ton of revolutionary technological breakthroughs that are never mentioned again, like Genesis and soliton waves and quick-cloning and ways to preserve the mind after death. (Although we did see the occasional Primeverse discovery that had an ongoing impact, like the Doctor's mobile emitter, itself a future technology. ENT implied that Starfleet obtained photonic torpedoes from the Vissians. And the novels have shown quantum slipstream drive, a technology of Delta Quadrant origin, coming into more or less regular use by the Federation.)
And I would submit that V'Ger may indeed have pushed Starfleet to become more military. They certainly seemed more military in TWOK through TUC than they had in TOS, TAS, or TMP. And by TSFS, they
were building a bigger, more imposing ship, the
Excelsior. We also know that nearly a century later, the Borg threat prompted Starfleet to build up its ship numbers considerably and develop new, more combat-geared ship classes like the
Defiant and perhaps the
Sovereign, and that the peaceful, exploration-focused Starfleet of early TNG gradually developed into a more combat-oriented body in response to the threats of the Romulans, Borg, Klingons, and Dominion. And since we never heard of Section 31 until late in DS9, it seems plausible that they increased their activities in response to the Dominion threat.
I also question the assumption that bigger ships would be more military-oriented ships. If anything, I'd think that you'd want combat ships to be more compact so they're more efficient and don't present as large a target. Maybe the technological advancement just allowed Starfleet to build bigger and more powerful ships for exploration or colony-support purposes, just as their ships are bigger in the 24th century. I mean, the
Galaxy class is the largest Starfleet vessel class I'm aware of in the Primeverse, and it was created for long-term exploration first and foremost, and for fighting only as a last resort.
By the same token, the advance in technology would itself explain why alien races were encountered earlier. If ships go faster, they can get to distant planets sooner. So you're not really listing three different things whose causes trace back to Nero's arrival, but only one thing -- the technological advancement resulting from reverse-engineering the
Narada's tech -- and two of its direct consequences.
Of course, that leaves the question of why the Starfleet/Federation of 2233 and after would've been so much more motivated to reverse-engineer alien technology than those of later eras in the Primeverse. Maybe it's just a matter of the policies of the people in charge at the time. Maybe the head of Starfleet, or the Federation President, in the 2230s was someone who had a strong desire to push technology forward by studying alien tech, but in the Primeverse they didn't find any alien tech much more advanced than their own, not until after that person's tenure had ended. Maybe later authorities felt that the Federation should apply a sort of Prime Directive to itself and resist advancing its tech too quickly. If you have any doubt about how quickly a nation's policies can change with a change of leadership, compare the George W. Bush administration to the Barack Obama administration.
There's more to just the things you mentioned though. Why do the Klingons look different?
They've looked different many times before. They had a couple of different makeup designs in TOS, then gained one type of ridges in TMP, then a different type of ridges in TSFS, then a subtly different type in TNG and after, then another different type in TVH through TUC. (For instance, in the movies, female Klingons have much smaller and more delicate ridges than males, but in the TV shows, their ridges are just as prominent.) This new variant isn't substantially more different from the past three major Klingon designs than they were from one another, aside from the blue eyes and the piercings.
We've already seen two different types in "Arena" and "In a Mirror, Darkly." The novels have claimed that the Gorn genetically engineer themselves into different forms.
Why has Praxis exploded...
There's a "classified document" out there as part of the film's viral promotional material implying that Section 31 may have undertaken a "Praxis operation" that might've caused the explosion. Although it could be that the Klingons themselves accelerated their ship production after the
Narada trashed dozens of their ships, and that this caused the explosion to come sooner.
Personally I think red matter traveling through time did more damage to the timeline than Nero appearing in 2233. Like how Q's anomaly in All Good Things messed with genetic development on earth, Red Matter might have caused subtle shifts in important places for things to change and happen differently.
Red Matter after all was an unknown quality even at the time of its creation.
Not sure that's necessary, but it's an interesting thought.