The mechs were built in Archimedes' timeline
Archimedes says he's yet to find another timeline as advanced as his was, and in every playthrough Jessica Kern the CEO of RST notes that the mechs are beyond current technology despite dismissing their claims as time travellers.The Renfield bombs don't actually destroy the hives, they just transport the Vek into another timeline
It's mentioned that the Renfield bombs use the same 'breach' technology the player uses to go back in time or to go into other timelines. The Vek that get hit by the bomb don't die, but instead are transported into harder difficulty settings. The Normal and Hard campaigns are actually timelines where the Vek got reinforcements from other campaigns where the commander won. This also means that there are timelines where Earth is completely infested with Vek. Alternatively...The Renfield bombs kill the Vek by transporting them into a timeline where Earth is completely uninhabitable
The bombs do so by just sending the Vek into a version of Earth that's either irradiated, covered in ACID, unbreathable, etc.Pilots who get traded for Reputation get their own happy ending
When you finish an island, you can trade a Pilot for more Reputation. That Pilot will stay back and guard the island. If you succeed in detonating the bomb in the final mission, the Pilot you 'sold' will get to live in a world finally free of Vek.