I'd love to run Backyard Baseball but have no way of recording my gameplay. How did you record your WR?

I use oCam to record, it's free and unlike most free recorders, this has no watermark on recordings. There are better options to record if your willing to pay though.

Another question would be how am I supposed to put a timer on the video? Because I'm in the ScummVm screen, my hotkeys won't work for the split timer that I downloaded.

Depends on which timer you're using. Most runners use LiveSplit for their timers and for LiveSplit, or those similar to it, there is an option you need to enable to used hokeys during gameplays. This option is Global Hotkeys in settings, or something similar.