Graphene OS - best privacy and security, only for Google Pixel phones

Calyx OS - less secure but supports cheaper phones (Motorola) and eco-friendly phones (Fairphone)

Honorable mentions are LineageOS, /e/ OS, Replicant and iode OS, however their security is much worse than of Calyx/Graphene (no verified boot), so use at your own risk

Yes, they exist, but there is no reason to use them other than tinkering around. Also they have much worse security than Android or iOS. So if you need something private and open source there are a plenty of degoogled Android ROMs.

They are not called tankies because of rolling tanks though

The term “tankie” was originally used by dissident Marxist–Leninists to describe members of the Communist Party of Great Britain (CPGB) who followed the party line of the Communist Party of the Soviet Union (CPSU). Specifically, it was used to distinguish party members who spoke out in defence of the Soviet use of tanks to suppress the Hungarian Revolution of 1956 and the 1968 Prague Spring, or who more broadly adhered to pro-Soviet positions.[6][7]

From Wikipedia