Not false, you sir should go ahead and do your own research.
1. A 107 certified Remote Pilot may receive a waiver which may or may not require them to get ATC authorization to fly depending on the limitations of said waiver
2. Anyone may not fly in class G airspace without providing prior notice
, you are wrong here as well. Section 335 (a) (5) says
"(5) when flown within 5 miles of an airport, the operator of
the aircraft provides the airport operator and the airport air
traffic control tower (when an air traffic facility is located
at the airport) with prior notice of the operation (model
aircraft operators flying from a permanent location within 5
miles of an airport should establish a mutually-agreed upon
operating procedure with the airport operator and the airport
air traffic control tower (when an air traffic facility is
located at the airport))."
So if the class G airspace is withing a radius of 5 miles from the airport you MUST provide prior notice of the operation. This is what the OP was asking about.
3. Yes it is possible to get a waiver for up to 4 years, here is the link to the
Waiver/Airspace Authorization Instructions. Also here is a screenshot of page 3 of those instructions in case you are too lazy to look for yourself:
View attachment 74291