Did the Russians copy any military stategy,arms,etz...from the Mongols?

Answer 1

Close, but not exactly. The Russians had a large number of Mongols (although a more correct term, given the time frame, would be Tatars) in their service, so they incorporated the know-how along with people that possessed it.

After Islam became the official religion in the Horde in 14th century, many dissidents (primarily Christians) began to flee to Russia, where they were accepted into the Russian service and were allowed to marry Russian women. By mid-1400s, religious persecution turned into a political one, so Muslims who fell out of favor began to leave, too. In 1450s, Vasily II, the great prince of Moscow, allowed the dissidents to form a khandom in the city of Gorodets, about 150 miles south-east of Moscow; in 1471, Gorodets was renamed into Kasimov, to commemorate Kasim, its first khan. With the formation of the khandom, escape into Russia became even more attractive for many of the dissidents still remaining in the Horde. The army of "the little king of Kasimov" was used by the Russian crown against both the Horde and Lithuania...

Answer 2

Yes, the light cavalry tactics.
Read about the Cossacks.