What pipe do you mean? The 1-2 pipe to GO to -1 or the pipe IN -1?

Dock the Switch, and you should be able to capture it with any HDMI capture device. If you don't have a HDMI-capable capture device, or just don't want to dock it.. there's really no other way then to just point a camera at the screen.

There are a few games with autosplitters, and then some that have an IGT system (although a lot of these games switched to RTA timing, too) There are also other runs timed RTA that you might as well not framecount (for example, if the run's over 25-30 minutes, there's a pretty good chance that they won't even display the millisecond timer here on Speedrun.com). But, if it's a shorter, more optimized run without an IGT system, you'll have to framecount. There are multiple ways to do this. There are freeware programs, like Avidemux, that show the current frame you're at (which makes it way easier to determine how long the run really was), and even VLC has a way of doing this (although VLC does not display this option by default, you can enable it via a menu option: View > Advanced Controls, and then there should be another row, the last button is a frame-by-frame button)