There was Chimeran technology under the planet the entire time, but how could there be if the Chimera were created by an alien virus?
There are hints that the Chimera have come to Earth before. Perhaps those early Chimera left it behind.
Outright confirmed in 2, when Daedalus and Malikov both refer to aliens burying their stuff here millions of years ago.
Where was the tower in New York dragging Earth to? Is there some sort of larger Chimera collective?
At some point there was. However, by the time the Resistance series takes place, it seems likely that they've been almost or entirely wiped out. The tower links back to the Chimeran homeworld, but in all likelihood there's nothing alive on it.
Why did some Chimera go feral?
The death of Daedalus fractured the Chimeran hivemeind. The more organized Chimera managed to stick together, but the less easily controlled strains broke off.
Where did all those alien plants come from?
Maybe the Chimeran virus mutates plants as well.
How did the humans rebuild New York City with only a tenth of the population?
They're probably not rebuilding everything.
Why was Capelli dishonorably discharged? Hale had turned into a Chimera, what else was Capelli going to do?
Changed or not, Hale had still accomplished a lot for the human side, and they were probably discouraged to see him go. Also Capelli was known to be a hothead so they might have thought he killed Hale needlessly when he could have been brought back and used as a source of information.