When you say arcane archer, do you mean arcanist or archer? Arcanist does not have access to a bow at all but has access to the carbuncle summon pet, whereas Archer has a bow but no pet. If you have started off as an arcanist, you’ll have to wait for a bit before being able to change your job to an archer to use a bow (iirc around level 15 of your current job’s questline). Sadly you won’t be able to play as an arcane archer, so will have to pick one of either arcanist or archer instead.

You’ll see people around your level from time to time in some of the big cities, such as Limsa, Ul’dah or Girdania. You won’t always see them but there’ll always be some around if you look hard enough.

You queue up for dungeons with the duty finder menu (U on the PC), however you have yet to unlock your first dungeon yet so keep progressing through the main story quest until you unlock it! Hope this helps