Welcome to ffxiv! To answer your questions....

1. When you reach lvl 10 you can change to new classes after accepting the short quest at each classes home area. For example if you want to change from lancer to gladiator, you will need to go to the coliseum in uldah to join the gladiators guild. After you talk to their guild leader and join, you van then equip a gladiator weapon and change your job in that way.

2.dungeons require 4 people to complete, 1 tank 1 healer 2 dps. Fun fact, duty finder takes forever to find a group with unless you are a tank or healer!

3. To become a paladin you must achieve lvl 30 gladiator and lvl 15 conjurer. You must also complete all of the class quests for gladiator up to lvl 30. After this you can receive a quest to become a paladin. Note that jobs share levels with the classes they are built off of. So your paladins level will always be what your gladiators level is and vice versa.

Hope that helps you out!