You can definitely visit during that time. You may face high altitude problems while going to the Gurudongmar lake only.

Yes. But need a permit. (Issued locally)

Yes but u can view snow kala pathar is near from chopta vally.

Oh yes, very much possible as roads are good. Just be careful about acclimatization for at least 24 hours, before reaching this lake as air is thin and one gets dizzy due to lack of oxygen.

Villages on the way are very very small. I don't think there would be any place to stay en route. All the bikers whom we met at Gurudongmar were staying at Lachen. My suggestion would be to base yourself at Lachen and make a day trip to the lake and back. Incidentally, we found a few bikes struggling to make the climb - their bikes were not getting sufficient oxygen at that height!

No health risk if you are healthy and fit. The 45 mts stay at the lake is well manageable. Carry biscuits and bars or have tasty noodles at Thangu. But the road condition is too bad, be it car or bike.. For bikers, no doubt, so much adventure awaits them.

International tourist can be allowed with permission

You cannot go to muguthang Valley as no Permit is issued for the same.the road to muguthang Valley valley is under construction n is looked after by the border road organisation.