1. Is the problem that the ocsillator is unstable or can it be adjusted with the OSCTUNE register to work ok?

it could be adjusted, but for any serial communication, i never trust any internal oscillator, i prefer to use a crystal instead. The internal will shift with temperature, gas price, wind direction and so on. Using a crystal allow to sleep really well all night


2. It says on page1 of the datasheet that you don't need a crystal for RS-232. Is this not true?

Not false, not true, this will depend of the environment and how lucky you are.


3. As the 16F88 only has 1 AUSART port is it better to use it for RS-232 or SSP.

It's two different animal, MSSP is used to interface I2C and/or SPI device, while USART is just plain serial communication, synchronous or not.