X15-65804.iso is W7 Pro and yes you can burn it to a DVD. I recommend using
ImgBurn to burn it. You still need to know your license key so I hope you have that. You should not need your XP disk.
BTW: x86 means 32-bit, x64 is 64-bit. If you want W7 Pro 64-bit then you can download that. In fact even if you want the 32-bit you may want to download to get the W7 SP1 version, otherwise you install and then download updates for a good while. So yes use the sticky thread for W7 SP1, either bit-size,
HERE (you must get PRO because that is the key you have but it is good for either 32 or 64-bit).
Never tried it but the Microsoft tool mentioned
HERE can burn to DVD or send it to a flash drive, which was one of your other questions.
New machine: Will it activate, yes. It may be necessary to call Microsoft and say that you made some changes to your system, etc and that is generally good enough for the person on the line.
As for legality ... well that depends on what license you bought. You likely bought an upgrade license which means it falls back onto the XP license, so if the XP was OEM then it was limited to the life of that specific motherboard and/or computer. If you bought the full version or if your XP could be transferred to another machine then this W7 can be transferred. (This may be a little basic, I'm sure it's more complicated but this should convey the basics of it. We @ W7forums can not and do not recommend anything but using it legally)