No, you cannot form a federation with structures that belong to different players. Based on the rules provided, federations are formed from your own structures only. The rules state that you "Form a Federation" as one of your possible actions, and all references to federation formation refer to connecting your own planets and structures together, not combining structures with other players.

No, you cannot build on a Gaia planet immediately after starting a Gaia project on it. The rules show that "Start a Gaia Project" and "Build a Mine" are separate actions listed under the Actions phase. Starting a Gaia project places a Gaiaformer on the planet, but you would need to take a separate "Build a Mine" action in a later turn to actually colonize that Gaia planet once the Gaia project is completed.

No, you cannot research beyond level 5 in any research area. The rules show that research areas have levels 0 through 5, with advanced tech tiles placed "on each space between level 4 and 5 of the six research areas," indicating that level 5 is the maximum level for all research tracks.