The X-rays themselves in the concentrations used shouldn't cause a problem to video tape; it's the magnetic fields generated by the X-ray machine which is more likely to affect them. Fortunately though, most of the modern X-ray units have lower magnetic field strengths than in the past, and one or two passes are unlikely to cause problems. If you kept passing a tape through the machines over and over you might start to notice degradation of the picture and sound quality though.
On the TV/VCR compatibility issue, many current-model VCRs here do provide NTSC-playback facility, but not all, so check before buying. They generally do not convert the picture format, but output it in normal 525/60 American format, so the TV needs to be capabale of displaying that as well. Just about all current production domestic TVs have at least one SCART connector on the rear and/or independent component video inputs on RCA jacks, and most will accept a 525/60 video signal on these just fine, although sometimes the picture size may alter very slightly so that there's a little overscan or a small black border top and bottom or at the sides.
