The hardware is capable of 9 data bits but at least the standard ATmega hardware serial library doesn't support more than 8 data bits, so I doubt that the developer of the core for the Tinys added that feature. Of course you can add that feature yourself (that's one of the benefits of Open Source software!) but I'm not aware of any ready-to-use library for the Tinys.
Yes, that hardware handles that automatically.
The parity bit is processed by the hardware, so you cannot use it as a replacement of the 9th bit.
The hardware has support for that 9th bit, you can find it in the UCSRnB register.