Leaving him the gun creates a whole lot of risk that he would lose a valuable weapon.
If Raynor did kill himself, obviously he would keep lying to Kerrigan until she found out the truth. As he wanted to have a showdown with her, we can only assume he was deranged as a result of Narud/Durans influence.
You're correct about what happened after Brood War. Personally though, I feel it's just such an awkward, complicated backstory that's not fully explained in Heart of the Swarm. The writters could have tackled it better.
They wanted him for the coolness factor and to give the Swarm a bit of humanity. Like Kerrigan, he possesses power far beyond what the Swarm is capable of (because he was experimented on by servants of Amon). He is also capable of feeling compassion for humans like the new Kerrigan, unlike all other Swarm commanders (although Kerrigan is working on that). These factors make him a very good ally to Kerrigan who will help stop her reverting back to her old ways.
There is also that hint of mystery to him. Why was he allowed to escape? Perhaps he got lucky and desperate and needed to stop Amon's plans. Perhaps he was allowed to escape as part of Amon's will and is in place to betray Kerrigan in LotV. Only time will tell however we can be sure to see him again in LotV.
Also, I have a relatively old computer and it doesn't run Starcraft II very well, so every time I load up one of these missions it takes quite awhile. The whole process is quite frustrating for me.
The missions themselves are about a 5 minute job. There is no real way to fail them (it instantly resets to before a task). They should also load in a couple of seconds if you have been playing the game recently, if they fail to do so then your computer must be running out of memory for cached files. Inserting an extra 1-2GB of memory would fix this and make the maps load considerably faster.
and doesn't have the might of an entire UED Fleet aligned against her.
Actually that was just a small UED task force, not a UED fleet. It was sent without any real firepower and equipped with only very light weapons on the premises that they could take control of local forces (both Terran and Zerg included) which is where their firepower came from. With local the local Terran fleets and Zerg at their control, they did not need to send in their real fleets.
Ultimately its destruction was insignificant compared to the actual UED fleets. The reason a replacement taskforce (or a fleet) has not been sent already is that the UED is meant to be having internal political conflicts which is causing quite a bit of confusion over territories and priorities for their military. Add to that Mengsk being very planning and you probably have it that the Dominion has been sending false reports back to the UED, tricking them into thinking they do not need to send reinforcements.
The fact is the UED are meant to be insanely powerful. They are probably so powerful that the Zerg Swarm would be no match to them (Kerrigan trying to attack Earth like she did Korhal would be stopped long before she even reaches the solar system). They could probably stop both the Protoss and the Zerg in their current states without even using their entire fleet.
So how come all humans die if Kerrigan was to have been killed in WoL? It is unclear if the battle focused on within the Galaxy and the Humans the Protoss knew about or if the UED really was destroyed there (only was going to be destroyed next). However what is clear is that Amon is extremely powerful, possessing knowledge far beyond anything the Protoss, Zerg and Terrans (Dominion, not UED) can achieve. With full control over the Zerg and his Hybrids to control them, he probably would have expanded massively until even the superior power of the UED could not drive back the overwhelming numbers.
One of the game developers said it was quite possible that the UED possess "Death Star" like weaponry on their battle-cruisers, where the forward cannon can destroy planets.
Remember that the Terrans of the Dominion were all settlers that came from criminals. All their base knowledge was that of a subset of what became the UED and due to "third-world" development probably progressed far slower than the UED. I would not be surprised if UED military units are shielded like all Protoss units.
On a side note, what was with that Psi Destroyer thing on Korhal? Mengsk unveils his big secret weapon and it does next to nothing.
It was not on Korhal, but floating above on a platform. The idea was it would emit an ever expanding shield that would eventually cover Korhal forcing all Zerg off the surface and thus stopping the invasion (until their fleets could break through and save them). It is unclear if it was one of Narud/Duran's creations or not (as he would have done anything to get Kerrigan killed as she is a threat to Amon) but it obviously something that the Terran possess the knowhow for (like how the UED can build facilities to locally control the Swarm).
It works by putting huge feedback through psionic links. In the case of the Zerg Swarm this is the connection between all Zerg and their commanders (used to be cerebrates and overmind, now its queens). The result is they literally destroyed by it if they enter the field. Since Kerrigan has such a Psyonic link to control the Zerg she is hurt heavily by it and even short exposure could fry her mind. Since the psionic link that controls the Swarm was a feature added to the Zerg by Amon, the Primal Zerg have no such thing and thus were not affected by it.
Stukov could possibly have also stopped the generators since I doubt he had a very strong psionic link but they needed to use that stupid Primal Zerg guy as otherwise he was excess baggage on her flagship. Also I think you were meant to use all heroes at once originally but that was axed so they had to get the Primal guy to make some appearance.
On a lesser note, the Psy Destroyer field would also work on Protoss as they also have a universal psionic link, killing all normal Protoss who enter it with ease. This includes their Zealots, Stalkers, Immortals, Dragoons, Scouts, Void Rays and everything else that is manned by normal Protoss. High Templars, Dark Templars and all their robots would be unaffected by it for the logical reasons that they have no psionic link.
In case you referring to the artefact in Mengsk's throne room, then that is a different story. It is basically a large psionic drain that sucks psionic energy from anything psionic nearby. Since Mengsk and Raynor do not have strong Psyonic abilities, they feel nothing at all from it. Since Kerrigan is a very powerful Psyonic being and a Zerg queen (who uses Psyonic links to control all Zerg) she would be very badly affected by it, weakening her to such a state that she would probably die.
It basically worked, Mengsk won as Kerrigan was powerless and cringing, if not for one variable he never considered. Despite all that Kerrigan did, despite all that Mengsk torched Raynor about Kerrigan, despite Raynor being heart broken, Raynor still was behind Kerrigan and came in at the last minute to save the day, shooting the remote control from Mengsk's hand allowing Kerrigan to finish him.
This is also meant to prove all the full Zerg commanders wrong with their beliefs. They were for ever saying how pathetic the humans are and questioning why Kerrigan was so merciful to them when she clearly was so much more powerful than them. They would have killed every human, Raynor included if they could. However in the end their all powerful queen, representing the pinnacle of Zerg achievement, won by not being Zerg but by being Human, and keeping her Human promises with Raynor who came in to save her. One can imagine that the Zerg will forever see Humans in a new light, as equals rather than inferiors like they had in the past. This paves the way for a galaxy peace at the end of LotV, where the Terran and Zerg will be friends and respect each others existence.
On a miscellaneous note, the Artefact would work to not only stop Kerrigan, but Zeratul and any Protoss Templar as well since they are also heavily Psyonic.
