Jenova

One of the current requirements the game has for a username states there must be at least 3 characters, so just "J" would not work. However, certain special characters (hyphen, period or underscore symbol) can be included in a username as well.
 
Also, you can create multiple accounts that share the same email address.

Patrick addressed this topic in an old thread and provided a detailed explanation which you can find here: https://forums.pokemon-vortex.com/topic/26874-what-are-the-requirements-for-each-forum-rank/
But to briefly summarize, anytime you actively use the forums- whether it's to create or engage in meaningful discussion about the game, you are awarded points through those interactions with you and other members. With time as you continue to do so, your ranking will gradually change. 

Yes. Beast Balls have a 100% capture rate solely for Ultra Beasts. 
Additionally, Vortex Balls also have a 100% capture rate and can catch any Pokémon, including Ultra Beasts.

The number of battles is not an accurate measure as to how much total exp a player is expected to have. Factors such as purchasing Pokémon with high exp from an auction, or another account training the Pokémon and giving it back will affect the total as well.

It means that the person who originally caught the Pokémon has been banned.