One of the curious questions is whether or not Patriarch Kirill is merely Putin's puppet and, in fact, not the legitimate patriarch of the Russian Orthodox Church.
If he were Putin’s puppet he would have recognized the Abhkahzian Orthodox Church and the Orthodox Church of South Ossetia, but Patriarch Kyrill continues to recognize the Church of Georgia as the sole legitimate ecclesiastical authority in Abkhazia and South Ossetia, which is obviously contrary to the wishes of Moscow.
If so, then where would find the legitimate Patriarch? During the Communist years (and actually in centuries preceding them as during the time of the Old Believers) the legitimacy of the Russian Patriarchate was rejected by many Russian Orthodox faithful, often at a fearful price.
Forgive me, but you are somewhat misinformed. The Old Believer schism happened in the 1660s, and has largely healed: since the 1800s, the canonical Russian Orthodox Church has sought to reconcile with the Old Believers, and since the office of the Moscow Patriarch, which had been uncanonically usurped by Czar Peter after the repose of Patriarch Nikon, was restored in 1917, further progress has been made. There are two independent Old Believer hierarchies, one of which has a Patriarch and one of which I believe is led by a Metropolitan, but relations between them and the MP are improving. During the Soviet Union, the Soviet government focused on persecuting the Russian Orthodox Church itself, and as a result the Old Believer jurisdictions arguably enjoyed better conditions than during the 18th and 19th centuries, when they were subject to arrest and violent persecution, and also were not allowed to ring church bells. They survived, like many religious minorities, through success in business, which prompted Czar Peter to implement a “Beard Tax” in an attempt to suppress them
Now, during the history of the Soviet Union, almost all violent persecution of the Church occurred under Lenin and Stalin, with some violemt persecution under Kruschev, and mainly oppression under Brezhnev and the other successors. Now, the actual history is this: initially the MP was completely persecuted, and after St. Tikhon died in prison, there was no Patriarch appointed to replace him.
Instead, the Soviet union collaborated with a group of liberal bishops known as the Rennovationists, who sought to impose a radical reformation on the Russian Orthodox Church, by eliminating monastic bishops and replacing them with married bishops promoted from the priests, radically changing the liturgy, and promoting Soviet ideology. The Rennovationist Church was extremely unpopular, and with WWII approaching, Stalin realized he would need the support of the legitimate church to survive it. Thus he pledged to stop persecuting the Russian Orthodox Church in return for Metropolitan Sergius, who became Patriarch, pledging loyalty to the USSR, which he did. This peace lasted until the end of WWII, when violent persecution was resumed.
This was unacceptable however to the Russian Orthodox Church Abroad, or ROCOR, which broke communion with the MP and anyone in communion with them, and remained canonically isolated until 2007, when it reconciled with the Moscow Patriarchate. ROCOR is also associated with the “Catacomb Church”, which was a legitimate, underground component of the Russian Orthodox Church which did things in secret things which could not occur officially, for example, preaching, and catechizing children, and operating in certain places where the Soviets had closed all the churches.
The Moscow Patriarchate, in addition to the covert alliance of its clergy with the Catacomb Church, had an above the table relationship with Billy Graham, who was officially invited and given a blessing to preach in Russia, and he did this repeatedly, and this helped the church considerably, and thus Metropolitan Hilarion Alfeyev, who is in charge of ecumenical relations at the MP, and is also a talented composer, was present at the deathbed of Rev. Billy Graham. The MP also had an official relationship with the Metropolia, a grouping of Russian Orthodox churches in North America including all the churches in the massive Archdiocese of Alaska, which consists of a great many Aleuts and other Native Americans converted to Christianity by the Russians, and this became the Orthodox Church in America, which the Moscow Patriarchate granted autocephaly to 1970, something also recognized by the autocephalous churches of Bulgaria, Poland, Georgia, Serbia, the Czech Lands and Slovakia, and I think the Antiochians, but not by the EP, or the other churches that recognize the Orthodox Church in Ukraine. The greater number of Russian Orthodox churches in the US are a part of the OCA, which is completely independent of Moscow, but the OCA also expanded and accounts for about half of the Bulgarian and Romanian Orthodox Churches, and also a bit more than half of the Carpatho-Rusyn Orthodox Churches. The other half, in a pattern which seems to repeat itself, are part of an autonomous church under the Ecumenical Patriarchate, the American Carpatho Rusyn Orthodox Diocese, which like most autonomous churches under the EP, has a Greek bishop rather than a Carpatho Rusyn bishop. The OCA has had multiple Metropolitans of Carpatho Rusyn ethnicity.
ROCOR and the OCA have substantial Ukrainian membership, and are substantially larger than the Ukrainian Orthodox Church in North America, which is also under the Ecumenical Patriarchate. Despite this, and despite ROCOR and the OCA donating massive amounts to help Ukrainian refugees in Poland, and despite the fact that the presiding bishop of ROCOR, Metropolitan Hilarion Kapral, memory eternal, who reposed in late May, was a Ukrainian Canadian, ROCOR and OCA churches in the US and elsewhere have been vandalized since the conflict began, despite being the churches where most Ukrainians are worshipping, as discussed here:
Vandalism of Russian Orthodox Church in New Zealand
Now this thread in the Orthodox forum address several of the issues you have raised:
UOC-MP is seeking relations with OCU