Why are they trying to avoid the Council noticing them?
Because aside from Optimus none of them are qualified by them to take care of the groundbridge crisis and he was forbidden from doing anything after the battle on Nemesis. He can only be included once the Matrix is returned to him.
Wheeljack starts it all and does it basically by breaking into Optimus' house. Threatened by the Prime calling the authorities on him he reveals his plan of making an experimental spacebridge that would help him search the universe for his friend Bumblebee. Optimus himself grows impatient with Ultra Magnus' promises of returning Hot Rod and the Matrix so despite the orders he decides to help. It's only a matter of time until the rest of the group joins in and begins their secret project