Do I have to enroll in a political party?
No. You can choose "No Party" and not be affiliated with a political party. However, NY is closed primary state which means you will not be able to vote in any primary elections. Primary elections are used to narrow down the field of candidates in a single party. For example, in 2020 there were over 20 Democrats who wanted to be the presidential nominee and those were narrowed down to one, Joe Biden, through primary elections.
Can I change my political party?
Yes, you can change your political party at any time using the link above.
If I register as a party member, do I always have to vote for that party?
No. In a general election you are able to vote for whoever you think is the best candidate. However, you are restricted to the party you identify as in the primary election.
Selecting "I need to apply for an Absentee ballot" allows you to have a ballot mailed to you if you cannot access your voting location on election day. For example, maybe your permanent address is in Liverpool but you are in college for four years in California.