Hey man, I don’t want to discourage you, but this is one of those things where if you have to ask how to do something you’re probably not experienced enough to do it. That being said, as a learning opportunity even if you don’t make it far you’ll still learn a lot about how GPUs work.
I’d start by looking at any existing drivers you can find and see if you can document or find documentation for the commands fed to the GPU. From there you can look at the Mesa project for examples of converting Vulkan to instructions for specific processors and see if you can get it to all fit together for your project.
From what I recall the completely fair scheduler (CFS) used by default on most Linux systems has a lower average latency than the RT kernel. The RT kernel just gives you more consistency, hence the CFS having lower latency “on average”
So honestly for opening Firefox it’ll probably depends more on your SSD data rate, but in theory it’ll open faster on a “regular” distribution most of the time.
Real time is good for things like audio processing where having better guarantees that a process will get its share of the CPU is a benefit.