you don't have to rush to go down the pipe. Take your time and move one pixel at a time until you're far enough to go down it (remember not to move left at all). At least this way you'll see what it takes to enter the pipe.
The trick is to do a 1-2 frame input delay on your third chip placement. Good luck!!
I agree with @ShiningDragoon , you're probably slightly off center on your bat jumps, they're very precise.
Not sure about your main question, but have you checked all of your TV settings? Perhaps the resolution isn't set to 240p or is zoomed in. If not, it sounds like an overscan issue (very common for CRT and NES). Are there potentiometers on the back of your TV? If so, try adjusting those. Are you hooked up directly to the CRT or is there something in the middle (dvd player)? Does it cut all games off or just the one you're currently testing? Some games are designed to ovescan more than others. (you don't have to answer these questions, just something to ask yourself and check).
Hopefully you can just submit without having to fuss with the above...
Good luck!
The screen doesn't scroll backwards. Wall or not. Interesting idea though.
it will run at exactly 60FPS if you have V-Sync enabled.
You should practice on the Pellsson Rom. https://github.com/pellsson/smb/raw/master/smb-v5.6.ips
If you really live in Antarctica, I'd say it's allowed.
Vsync will probably solve your issue... but.. you're sacrificing FPS. Unless you're a sub 5 runner, I wouldn't worry about running at 60fps flat.
I notice you're using New PPU in FCEUX. What if you switch that to Old... and maybe switch everything else to default settings while you're at it, for consistency. You should also display FPS and Frames in FCEUX, to give more clues. This is interesting... ruling out settings would help us figure it out.
You need a capture card to convert the analog RCA signal to a digital USB/HDMI signal. Sounds like your best setup would be RF to TV and RCA to capture card to PC as @roopert83 describes above. You don't need a splitter with the way you're describing your setup. If you want two RCA output signals, then you'll need the splitter.
Does your video card have RCA female connectors? If so, you don't need a capture card. If not, you plug the cables into the capture card, and connect the capture card to your computer via USB (or HDMI potentially). Purpose of the Capture card is to deliver (and sometimes upscale) your NES video/Audio signal to your PC.