Mounts

[Johnist]

1. Is there any benefit to mounts, do you move faster or anything, or is it all about epeen?

Moving faster. That's about it.

2. Do you get to choose your mount, or do different quests offer different mounts.

When you acquire multiple mounts, you can choose between them.
The Gobbue Mount is exclusive to 1.0 players who acquired it in-game while it was offered then.
The LEGACY Chocobo Mount is exclusive to 1.0 LEGACY Players.
The Coeurl Mount is exclusive to 1.0CE, 2.0CE, and Digital Upgrade purchasers.
The Voidal Resonator Mount requires you to Subscribe for 90+ Days.
The Unicorn Mount requires you to be a White Mage.
The Company Chocobo Mount is the mount required to unlock the usage of Mounts in Eorzea. You obtain it by completing the side quest to hand over a Chocobo Issuance (2000 Seals purchase) from your Grand Company (unlocked after you beat Ifrit in Story Mode).
The MAGITECH Mount is awarded for completing the Main Story Line.

3. Is there an in game shop to purchase mounts?

At the moment, there are a limited number of mounts in game with various ways to acquire each.

4. Can we expect flying mounts in the future?

The Voidal Resonator mount is a 'flying' arihman mount, but it remains low to the ground. If you mean Flying high in the sky, I don't think so.