Surface Pro grounding issue
AC probing is safe so long as your multimeter is rated for the full AC mains voltage you'll be playing with, and the probes that you'll be using are insulation-rated for that voltage as well. Most reasonable-quality multimeters are OK for 120VAC work. Make sure the probe wire insulation doesn't have any breaks in it.

The meter will present a voltage measurement resistance in the megohm range, so there's no real risk of damaging anything (yourself, the meter or the tablet).