Firstly, welcome to Eorzea!
The posting restrictions are a result of a surge in spam that clogged the Beta test forum, so SE decided to head off any possible repeat in the official forum when the game launched by implementing similar restrictions. It's not too hard to deal with (especially the 1000 character limit is easily worked around).
Uh, as soon as you finish the initial tutorial quest in the Adventurer's Guild, you're free to go out and kill stuff if you so wish (in fact, the first quest for your class's Guild requires you to do just that!). There is nothing forcing you to go and do quests only in each town, although it's worth varying your time between slaughtering cute animals and helping out the townspeople with their problems. Also don't forget that side quests and main story quests have different icons - story quests have a meteor icon, while side quests just have a speech bubble like a letter 'Q'.
Technically though the game really opens up at around level 15 when as part of the storyline you gain the ability to use airships to travel between the three cities, as well as being able to start instanced dungeons in parties (which you have to do as part of the story).
A lot of people say the game really starts at 50 after the main storyline is completed, but really, the way the game is designed, the storyline unlocks content as you go along, so it's not so much the destination that's important, but the journey.
Personally I don't mind FFXIV's armour styles as it suits the setting - one thing I hated about games like WoW was just how utterly ridiculous a lot of armour actually looked. Here in most cases armour is functional and believable. Early on there's not a lot of choice when if comes to armour choices, but as you level up the choices and design variation for gear increases (particularly a lot of special dungeon gear has very unique designs so these are well worth aiming for). And then there's the whole vanity system that allows you to change the appearance of a piece of armour to another so even if you don't like the appearance of one item, you're likely to find something that appeals to your tastes you can use.
The game pretty much is this from the beginning - you're sent out on quests to kill things, as you explore and adventure you'll find yourself being drawn into the mysteries surrounding Eorzea and the meaning of that mysterious dream you saw at the start (and why your character keeps blacking out and seeing odd visions). There is so much more to FFXIV than just killing random stuff for junk.
There is PvP in the game - it's called 'The Wolves' Den', however it's party based (4x4 and 8x8). It requires you to have been advanced sufficiently in the storyline and thus you had to have joined up with a Grand Company in order to unlock it. Matches take place in a specific zone in La Noscea called, fittingly, the Wolves' Den. There is no 1x1 duelling in this game though.
As for mounts, I presume by 'dodo bird' you mean a chocobo. Well, this is a Final Fantasy game - chocobos are the series mascot after all!But don't worry, there are plenty of other kinds of mounts available. Some are bonuses that came with the Collector's Edition of the game (courel and Fat Chocobo), some are quested (unicorn), some are gained by simply subscribing for a certain length of time (behemoth), and some are unlocked after completing enough of the storyline (magitek armour), and many others I haven't mentioned. Bare in mind some mounts are now no longer available though as they were only offered for short periods and will never be offered again (Legacy chocobo and gobbuue).