How to vote in the New York Democratic primary (please share!)

Since these are party contests not actual elections do the regulations actually apply? (serious question from someone outside the country) From the article it sounds like a lot of things are messed up (54,000 registered members removed from the lists in Brooklyn as well as the above mentioned) and that court action is warranted but i would have thought that if the Party wants a closed primary then it up to the party members not the courts to consider the switch to a open primary.

If I started the Cow Party of America and the leadership rules said you get one vote per cow you bring to the convention and someone challenged this because they lived in a jurisdiction where keeping cattle is not allowed would this not be an internal cow party problem? The requirement to bring a cow to vote for the leader does not impact the ability to vote in the actual elections just in the internal leadership contest.