Simple answer -
It costs nothing to register an RTF.
You can register as an RTF.
The syndicate can also register as an RTF.
Is getting paid to be a passenger legal........I suppose there is nothing in the ANO that prohibits pilots paying people to be their passengers! (I know a few pilots who would have to pay me to be one of their passengers.
)
Providing training where you are the instructor (P1) is diferent from what you describe.
Remember that passenger time doesn't count towards anything but it is nice of you to volunteer to be a passenger with a pilot who you considder unsafe unless with an instructor having the authority to take control should something untoward happen.
It is illegal for a passenger to take control of an aircraft from the pilot!
Regards,
DFC