Convert measured spectrum to impulse response
Can I just write: X = 10.^(mag/20) .* exp(jphi/3602*pi) ?

Yes. If your software returns the phase in degrees, that's exactly right.
The tricky part is, however, the interpolation. The phase wraps round at 360 degrees. For example, if you have 1 degree and 355 degree, the correct interpolation would 0 degree (since 355 is the same as -1) but regular interpolation will give you 180 degrees which is about as wrong as you can get.
In this case unwrapping the phase often helps. You would start somewhere in the middle of the frequency spectrum where you have good signal to noise ratio and than unwrap up and down from there. Unwrapping means to look for phase jumps of more than 180 degrees and add/subtract multiple of 360 degrees to the phase until the jump is less than 180 degrees.
Another potential problem is bulk delay in the measurement which is fairly common for acoustic measurements. Bulk delay leads to very steep phase gradients which makes both unwrapping and interpolation difficult. This can be addressed by &quot;eye balling&quot; the bulk delay, take it out of the measurement. Then do the interpolation and inverse FFT and put the bulk delay back into the impulse response.