Russia, being at the crossroads of East and West was influenced by the Vikings – the first Tsars, the Rurik dynasty were Vikings, and the word Rus means viking.
Byzantium, Eastern Orthodoxy became the national religion, directly influenced by Byzantium – and the arts were directly influenced by the Orthodox Church.
The Ottomans influenced the Russians in terms of their expansion – the Russians and they wanted to expand around the shores of the Black Sea.
Persia – not much influence, although it was influential on many of the subject Muslim peoples of the Russian Empire.
The Mongols – the Golden Horde was the Khanate that controlled much of the land from the Urals to the Volga (and a fair bit more) and the Tsars owed them tribute – so they were Suzerain vassals of the Khan.
Part of the Mongol Empire in Russia was known as the Golden Horde (A???? ??? – Altan Ord in Mongolian), but it eventually splintered into were other Khanates – the Khanate of Kazan’, the Khanate of Astrakhan and the Khanate of Crimea and several others.