Well I cant start a run when im tabbed out of it.

Example: I don't do speedruns for on here but I speedrun among us so I have livesplit timer, I am tabbed into among us and not it but it is on the same monitor, and I press my mouse button to start a run but it does not start or same with ending, I have to tab into it.

Is there a setting that can fix this? Also, what's a good CPU for a low price? I might buy one

You're looking for Global Hotkeys. You can enable those in the LiveSplit settings - that will allow you to trigger LiveSplit even when it's not in focus (ie. when you're clicked on the game).

And as for that second part, that's a really vague question that doesn't have an easy answer. Usually just buying a CPU alone is....odd unless you're looking to upgrade or replace an existing one in your PC. But which one to buy depends entirely on the chipset you're looking to use. If your motherboard only supports Intel chipsets, then, well, you need an Intel CPU. Same goes for AMD. You're probably better off just googling your motherboard to confirm which chipset - and which generation of CPUs with that chipset - is supported and finding out which one to buy that way.

Granted some CPUs are better for gaming if that's the main goal of your PC, but again, that depends on the rest of your build and what your current components are.