Though idiot domestic in-laws are likely the reason Alexis II would want a European bride for his heir - "my son wouldn't have to put up with some idiots who want abundant favors from me just cause I'm married to their sister".
I think 1672 is the wedding year (18th birthday of Alexis Jr.), and 1673 is the earliest birthday date for son possible.
The second one is more likely, considering troubles Sophie Hedwig has converting into Catholicism (the reason she did not became the Holy Roman Empress) - though attitude of Lutherans towards "Papism" and Orthodox Christianity differed. Or it can be a princess from some minor house related to Denmark or Brandenburg dynastically, not necessary the main branch.
And given the Hohenzollerns and Kettlers are related, this match is the easiest for the Duchess of Courland to arrange out of the important ones.
Very true. Could this possibly lead to war later on?As for his policy towards the Commonwealth, the policy would be... mixed. On the one hand, the court reforms (clothes, etiquette, court entertainment etc) would be polonophilic. On the other hand, Alexis II is likely to be very distrustful of the Poles considering himself being "cheated" out of their crown, and this will play a part in his South-western policy, especially regarding TTL version of Eternal Peace.
The war with Turks (as part of big coalition) is just what is needed to modernize & train the army, thus avoiding fails like Narva later on when facing modern armies in wars with (2) or (3). So it will definitely be the big part of first half of Alexis II reign.
The "Amur crisis" (Chinese war of 1681-1689) is also a topic of the day, as with 1682 being just another year of calendar there is quite enough of free Streltsy and quite a few of them have ambitions worthy of small vacation to Siberia. This crisis also depends on Alexis II ability to push the reform of Siberian dioceses, as there was only one Metropolitan for entire Siberia, who sat in Tobolsk. The separate Metropolitan seat for Eastern Siberia (in Irkutsk) was created in OTL only when Peter I abolished the Patriarchy and thus it was the Tsar who appointed Archbishops/Bishops. If Alexis II is successful in creating Metropolitan seat in Irkutsk, that will allow better management of Eastern Siberia, thus somewhat better odds in this conflict.
It's much more productive to find a candidate for Patriarchy that goes along with the reformist plans (somebody like (arch)bishop Athanasy of Kholmogory -a modern-minded cleric, born in Siberia and thus understanding the issues of managing Church in huge country and not protesting the increase in number of bishopricks under the pretext that "it would make existing bishops feel less special"), than abolishing the Patriarchy institution altogether.