60FPS requires HTML5 player, and
I think it requires Chrome, but I'm not positive on that one.
I also thought I saw a 1440p60 video yesterday, but I may be mistaken. It's difficult to search because people keep labeling their videos stupidly.
While OBS is good to capture gameplay, if you want precision you'll need to use something else, like Fraps.
Not really. The trick is in your settings; FRAPS defaults to low CPU usage settings where possible, while OBS has slightly nicer defaults at the cost of being slower. If your CPU is too slow, lower compression (or even lossless) can make a big difference. Experiment with different codecs and see what works for you. If rendering is an issue, maybe avoid lossless because that'll need re-rendered anyway before uploading to YouTube unless you want to deal with insane filesizes that take forever to upload and burn through your bandwidth.
Personally I use Dxtory for capture, and
edit: and don't finish my posts? Huh.
Personally I use Dxtory for capture, and it works great—best performance I've gotten out of all that I tried—but I'm not sure it's got an overlay feature like you're looking for. One thing you can try is using other capture software
in conjunction with OBS. Any capture software that can output to a DirectShow stream (Dxtory for sure, maybe FRAPS?) can then be picked up by OBS, which can then add the overlay and do the encoding and writing and all that jazz. If the issue was in the capture itself, this should fix it.