it's all subjective. If it's geographical, then it's still dubious: Russia is 3/4 in the "Asian" part of Eurasia, so why doesn't it play in the AFF? Turkey is, what, 9/10 in Asia? Even the idea of "Europe" as a geographical entity is subjective and socially constructed, as it isn't actually a continent, but a small portion of the Eurasian continent. So is it tradition? Well then any side that's played in UEFA for a decent amount of time can be counted as having a traditional tie to UEFA. Israel's been in UEFA since the 1980s, which is longer than Russia has (since 1991, before that there was no Russian soccer team).
There's no possible objective criteria for membership, except for a country applying for and being granted entry into UEFA. That means every team playing in UEFA is legitimately a member.
no, but that's not a tournament involving national sides...it's a professional league championship. we do play them in the Baseball World Cup and the World Baseball Classic, which are the two major international cups involving national sides.