LTC5599: why are these baseband inputs passed through 49.9 ohms and the capacitor + SPI
For the SPI lines, why are there 1k resistors and 2.2pF capacitors? My
best guess is that it is to reduce emissions

Your RF output frequency is going to be around 1 GHz and that can easily couple onto lines used to control the chip (such as SPI) and so it's quite likely that the presence of the 1 kΩ resistors and 2.2 pF capacitors is to prevent this happening to a large extent.

Why are there 49.9 ohm resistors and a 100 nF capacitor to ground on
the BBPI/BBPQ differential pair?

I expect that these values can be increased but remember one important statement in the data sheet that relates to all the specifications that it contains: -

Test circuit is shown in Figure 13.

So, if you drift away from the recommended test circuit you jeopardize the specified performance. The price to pay for the inclusion of these components with the specified value is uncertainty. I would need to have a really good reason not to use the values specified and then I'd want to check with the supplier (AD/LT) the validity of any changes.