Few questions from a new player

[Bingopajamas]

Important loot drops are handled by a need greed pass system where jobs that can equip that gear can roll need, if multiple people roll need the drop is determined by a random generated number that is generated upon pressing need, the greed option is for players who can not equip the gear however need>greed so a need roll will beat a greed roll.
Mounts are unlocked by completing the storyline quests, you will be asked to join the grand company of one of the three nations, from there you can use company seals to purchase a chocobo.
To use a barding select it from your inventory and select use, then when you have a chocobo, go to your character menu and select companions, click it to open your chocobo menu where you can assign skill points, in the bottom right will be three equipment slots where you can now select and equip your barding.
Minions do nothing they are vanity items.