If they already had that Mass Relay they would have used it in the two year interval...clearly they had plenty of minions to activate it...the Geth and Collectors combined. Infact I find it rather odd that the Collectors weren't part of the first invasion....makes no sense. It would be lame to do another...lost relay...they've done it twice now and to go back to the same barrel...would be flat after what they achieved in the First Game.
The Collectors may have been formidable, but there's no way they'd have been much use in the Eden Prime War. All they appear to have is one base, and one very big ship...that's all. They're good at sneaking around and taking out defensless colonies and isolated ships but the Citadel fleet? No. Hell even Sovereign couldn't hold it's own against one of Earth's fleets. That whole battle sequence at the end of ME1 was just a mad dash to get the Citadel Relay open before the Reaper's kinetic barriers failed. The Geth on the other hand were recruited as canon fodder, so they were much more useful.
As for the rest, it's all under the assumption that Mass Relays are the only way Reapers know how to get around. They have been around for billions of years and I'm sure they have plenty more tools at their disposal than what we've seen already. Don't forget that the Mass Relay network was specifically created as a giant mouse trap, not necessarily as the Reapers' only means of getting around the galaxy.
Given what was going on with the stars I'll take a wild guess and say they're either collapsing stars to form singularities, wormholes or some such...OR they're building some kind of quantum entanglement teleporter.
As for the Human Reaper, it's not clear exactly what it's function would have been since there's still plenty we don't understand about the nature of Reapers. Whatever it's intended function, it's clear that just another run at the Citadel would be a bad idea. Plus they didn't want to build just any old Reaper, they specifically singled out humans.