(1) It won't affect your regen rate while resting. Food currently only has a stat-boosting effect. http://mooglebox.com/item/food.php has a nice list of what food boosts which stat. The game does have potions for instant healing in-combat, but they aren't very powerful. There are revamps of the food and medicine recipes in the works, so this may change when those are released.

(2) It will be possible, but you may have to wait until the next patch. The ability to reset them didn't make it into 1.20. If you look at dev1228 in the 1.20 Patch Notes, you can see what the primary stats do. For CNJ I put mine in VIT and MND.

(3) That's pretty much it. When you join a Grand Company you do get access to additional activities like company leves and caravan escort. A good way to improve the grind is to party with other players.

(4) Only monsters at your current level or higher contribute to a chain. This is another reason for leveling in a party, since it's easier to take on large numbers of mobs at or above your level in a group.

(5) This requires some knowledge of the crafting system. Raw materials like logs, fibers, skins, and ores should most likely be sold in the wards. If you set the price right someone will eventually want to grind that crafting class and will buy the cheapest ones, hopefully yours. If it's not raw material or gear, you can probably sell it, but you might as well wait until your inventory is getting full.

(6) CNJ and THM do not get any TP abilities currently. However, they can use TP through cross-class abilities. For example, many CNJs use the PGL skill Second Wind to heal themselves while conserving MP.

(7) That could be because your level is too low for the gear. If you equip an item above your level, it provides significantly reduced defense and none of the bonus stats listed in the box. All gear has an effect, and people spend a lot of time and effort getting the gear they want, but the most important piece of gear is definitely your main hand weapon or tool. For example, when I upgraded to the Cobalt Winglet (Attack 90) from the Cobalt Katzbalger (Attack 68), my damage went up on my GLA by at least 50%.

(8) Good luck! You might try the Cornelia world forums or try searching for one that you can tell is still active on the Internet.