Hi Craig McQueen,
Yes, the chip manual didn't describe that details which you mentioned, but actually, if you test the chip SPI, you will easy to know it.
Now, answer your several questions:
1 If the TX FIFO is empty, what is transmitted on MISO -- 0x00, 0xFF, or a repeat of the previous byte?
= I have tested it, it should be 0X00 if none data input to the transmit buffer, this is my test result

The yellow wave is the MISO, you can find it is the 0x00.
2 If SSEL is deasserted while the TX FIFO still contains data, is the TX FIFO flushed?
=

If the slave SSEL is not selected, I think the TX FIFO won't be flushed.
3 Can I flush the TX FIFO?
= You can write the TX FIFO, then when the Slave is selected, and the SPI_SCK come in, the TX FIFO data will be transfered.
4 Can I preload the TX FIFO with data while SSEL line is idle?
== Of course you can, just as I have said, you can write the data to the TX FIFO at first, then just wait the master's signal.
5 Is it possible to detect TX underflow?
==From the user manual, I find IMSC[TXIM]: Software should set this bit to enable interrupt when the Tx FIFO is at least half empty.
This may useful to you.
6 Can I get an interrupt as soon as the SSEL line is asserted? (so that I know I need to prepare data to be read). Either from the SSP, or from the PINT.
== You don't need to detect SSEL, you just need to detect the receive FIFO buffer, more details, you can check the SPI register.
7 Is it possible to configure a pin for PINT if the pin is configured for a function other than GPIO? Or, would I need to connect the SSEL line to a second pin to provide the PINT functionality?
==SSP module hardware don't have the SSEL interrupt directly, if you want to get the SSEL pin interrupt, you can connect it to the second PINT pin.
Wish it helps you!
Have a great day,
Kerry
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