Firstly you can edit a post after you've made it, and increase the amount of characters, as to not make multiple posts.
1-At lower levels, the stat difference between the rare and the common weapons, is NOT that big, however as the levels rise, it does become a noticeable increase from just a few points to closer to 10 points. What you look at for the rare Items is the Item Level. If you have a piece of gear that is level 15 from a Merchant and a piece that is level 15 from a Sastasha treasure chest, the item from Sastasha is actually = to a level 17 item instead of a level 15, the benefit is that it is an item you can use for a few more levels before it can be replaced.
2- For most MMO's there are usually only a few weapons that are available per level or for a level range of your character. What is different is that weapons in FFXIV are semi customizable with materia ( a whole new slew of questions will be asked about that I am sure ) So you can but a Sword that has 2 empty slots and either use it as it is, or add 2 pieces of Materia to it, maybe you want more Accuracy you can put that on it, maybe someone else wants a small boost to Damage so they put more determination on it. That is the primary reason there aren't a lot of weapons to choose from, you can customize the stats that are on them. Later in the game there are lots to choose from, and you will eventually find out there is always one that is Far better than the rest and FAR harder to obtian.
3- When you die, you gear deteriorates, as well as having to start back at the last place that was you homepoint. The Travel itself DOES have negative impacts as well, you automatically will fail an Leves or solo instanced duties upon leaving the area. Mostly its the gear deteriorating by a few percent, it can get expensive to repair your gear if you die frequently.
4-When I play on PS3 (rarely) I find that in battle the Up and down on the directional pad will select different party members and side to side will target different enemies, if you are in combat.
5- the two lines are for Gear durability and for spiritbond. Spirit bond, once full, allows you to convert gear ( must say convertable: yes) into Materia, which are gems that can be later affixed by crafters, to boost stats provided there are slots on the gear to put the materia in, there are exceptions but if you looks up the Materia system there is a lot of Info and I still don't have a 100% grasp on it yet.
6-For you chocobo there are Many ways to personalize it, at level 35 you can start to train it to fight along side you as a party member, and you can customize what role in the party it will play, or you can mix and match and let it pick what it wants to do by picking many different skills.( the last one will not allow you to choose a special rank 10 barding for specializing in one set of skills.) You can buy different barding from you Grand Company, also there is Barding that is crafted, and hugely expensive, from drops that come from doing late game content. You get Barding as a veteran reward ( subscribing for a long period of time. ) You can stable your Chocobo once you or your freecompany has a Chocobo stable where their house is, that allows you to train it with different food rewards that make it more prone to certain actions as well as give it snacks that will change it color if fed enough of the fruits.
7- Some Items have labels that mean they have limitations, they are Unique: you can only possess one of this particular item at a time, and untradable meaning you can't give it to another player or sell it on the Market Boards, it will display either or both of these at the top of the little window that describes the item. It's done to keep rare items feel special when you get them so its not something anyone can just buy.
8-The easiest way to find a FC is to put an advertisement in Party Finder, or to join parties and talk to people, you get invited to them very quickly if you show that you have a good personality.
9-Houses, they are a place you can personalize, if you get certian furniture you can teleport to your house, put gear in your free company chest, summon your retainer, hire vendors for your house, as well as have a garden to grow plants that give you access to materials for crafting and chocobo training without having to buy them, and it gives you a place to put a chocobo stable to train your chocobo or feed it to change its colors.
10- Fishing is like a mini-game its a challenge to catch rare fish, also it provides ingredients for crafts, cooking makes useable food, the food can give you boosts to your stats so say you make Mulled tea as your culinarian, you can use it on your Conjurer in a dungeon and you will get a % boost to Piety, determination and spell speed.
11- The template is to show you where the attack will land, it is not Auto hit, but you have to be outside of the template before it finishes "readying" or "casting" the move. There is a little bar up top where the monster's name and HP bar is that has the name of the move and a yellow line, when the yellow line reaches the other side, it finishes readying the move, if you are in the template when the move is readied, you will be hit, if you move out before the line finishes, it will not affect you.
Hope this helps.