Always happy to help with questions, so continue asking if you find more.

1. So to get one of those new hairstyles you need to do 3 things. First, activate the hairstyle book itself(right-click -> use if you play with a mouse and keyboard). Next, unlock the Aesthetician - this is done via the quest Beauty is Only Scalp Deep in Limsa. Finally, use a crystal bell to summon him to change your hairstyle - this is a furniture item you can find in your Inn room as well as many FC houses.

2. Already answered fairly well, the gold saucer forum on these boards also has some posts on this topic if you want more info.

3. Zetsumei covered this. When you press need or greed you automatically roll a number(which you can see on the loot window). Once everyone has picked, the relevant rolls are made public and the loot is automatically distributed. If you change your mind after rolling(decide you dont actually want something) you can downgrade your roll to a pass as long as the item hasnt been awarded yet(the opposite isnt possible - passing and then deciding you want it, so make sure before you pass).

4. Covered, but ill restate. Two is the maximum you get for free, while you can hire extras by increasing your monthly fee. If you do add retainers, they get added to every character on your account. Then once you do the venture quest Reinha mentioned, you assign your retainer an adventuring or gathering class, and they can go out on missions for you to bring back items that you decide on based on their level. They can only be classes you have unlocked, and cant level up higher then you currently are(also with the gatherers, they can only bring you things you have personally gathered yourself at least once). You pay them with Ventures(obtained several ways including quests and gc seals).

5. Generally, anything you get once you can get again. If you have inventory/retainer space then my advice would just be to keep equipment you like the look of. Crafting mats can be replaced, minions can be bought, mounts... are mostly untradable anyway, but a good looking glamour can be real annoying to have to farm. By the time you get to the really "priceless" stuff, you should mostly know what to look for anyway, so at lower levels my advice is focus on style.

Hope that helps!