A High Language is essentially an Upper Class or elitist language; it's seen as the language of preferment and no knowledge in it would result in very limited career hopes, as it were (the opposite being a Low Language).

That's correct. In exchange for protection, a poll tax and some restrictions (search for the Pact of Umar for a few examples although not that many were actually enforced) the non-Muslims were given religious freedom and were supposedly free of persecution but this was a theory and not always practiced/enforced. This obviously only applied to permanent settlers; Pilgrims and other visitors were generally left alone because they brought money to the economy and attacking them would damage that revenue. Also believe it or not Christian monks and priests were highly respected by the Muslims and were generally left alone (during Crusades and times of warfare this changed for the worse though).