At 1-2T this is bound to be superconducting magnets (or permanent over a very very small volume). The main field will vary only very slowly, on a time scale of minutes. The induced voltages will be minimal.
However, you should make sure that your cables do not move in the field, as it will have a strong gradient.At very high frequencies (MHz) yes. But you can perfectly well use coax cables for low frequencies and DC, then the magnetic part can be neglected.
In any case, even in a static (or slowly varying) background field you can still use coax cables to transmit high frequency signals.
Yes. The rate of change is more important than the absolute field strength. I know people that use twisted pairs (and also coaxial cables) in pulsed magnetic fields of 60T and more. Make sure the twist is nice and tight, with as little space between the wires as possible, and that the pitch is regular.
Note also that your magnet will have 1-2 T in the field center. The further you go away from that, the lower the stray field will be. IMR machines sometimes are compensated such that the stray field is very small.
NP