Here some answers and decisions I've made!
[list]
[*] There is a fixed number of giant monsters, but definitely more than one.
[*] There are lots of smaller monsters of all shapes and sizes, basically if you can imagine it, it exists.
[*] I will not retain absolute control over the monsters, whoever is closest to the giant monster will control it.
[*] It will be about 20 years since the last of the giant monsters came through.
[*] There are also medium sized Kaiju that are more numerous than the really giant ones.
[*] The giants and mediums really don't actively seek humans, they are instead driven towards population centers and usually live in the ruins of dead cities.
[*] The smaller monsters either hunt for food or just kill indiscriminately.
[*] I'm still working out exactly how to implement cyborgs/robots/Jaegers.
[/list]
If you have any more questions feel free to ask!