So, two effect enchanting - 1 gets me 55% magicka regen, the second gets reduced destruction and 10% magicka regen - do the two regens work together or does one cancel the other out?

They should stack for a total of +65% of the base regen rate.

The magicka regen & fortify magic school enchant is really weak. The magicka regen does not scale and the fortify magic school is weaker than when you use just fortify magic school.

However, when you max enchanting it can be useful to put reductions for the same school twice on one piece of apparel.