Part 1.
You can write cypher or gremlin queries that do what you want. Remember that you can traverse forwards and backwards on edges. Given a user, it should always be relatively constant time to pull up the last ten things they did.
Part 2.
If you are representing a band as an entity of a certain type, index on that attribute. Then you'll be able to pull out that node and traverse outwards to find all the users who like that band. If you don't have an independent entity, or it is somehow implicit, you'll want to enable full text search for your respective graph database.
Part 3.
Learn more about security. The only thing you would be storing would be a properly hashed string of the user's password. At that point you would be fine using any graph db and good security practices.
Part 4/5.
Once you have one user, worry about the next thousand.
When you have a thousand users, worry about the next hundred thousand.
When you have one hundred thousand, worry about the next million.
When you have a million users, you can start worrying about the questions you asked.
Until you have at least 0.1% of the users/volume you want to scale to, it's mental masturbation to try and ask questions about how to scale up to a certain size.