Yes to all the above
You may have display issues though, but you can patch the dash to work in NTSC if you softmod it or is modded in some other way otherwise it will display in PAL that your TV may not handle well or at all
Most PAL TV's now though can handle NTSC display without issue, but vice versa may be a different story
P.S. the xbox is region locked to start with unless you have a mod chip or a softmod in place, even with a soft mod the DVD drive is region locked, though once modded most games will run from HDD negating the DVD drive lock (DVD drives on the original Xbox are usually the first things to go anyway)