There are boards you can install in a computer, which capture video from a vcr, camcorder, etc.
However when you state PAL/NTSC format, it raises the question whether it is modulated, as for broadcast TV. I believe audio is incorporated into the signal. Therefore you must make certain that you purchase a board which is compatible with the signal from your source.
Once a video file is on your hard disk, you would run it through a video conversion programs Some are free. (Example, I use one called USBVision Exporter on my PowerMac, to convert mov to avi.)
You'll need to check specs to make sure a program outputs the format you want.
For the second half of your project, the same question from above applies. You can output analog video which is RF modulated, or unmodulated.
It depends on what equipment you are playing it on. If you have an old-fashioned analog TV, then it needs an RF modulated signal. (I believe this is the PAL/NTSC format.) In the USA, this would be on channel 3 or 4. Audio must be incorporated into the signal as well.
However newer equipment will be able to accept a 'composite' video signal. And still newer equipment might accept a better quality video such as S-video, and the type with separate chroma and luminance signals. These are analog signals. You would send the audio on a separate cable.
A digital monitor will produce better results than an analog monitor, when playing back a digital signal.