1.
The storyline seems to have changed the levels in which you acquire them, is there a new site that shows at what level you get them and where they are located? I don't remember getting the companion quest until 20 last time, but picked it up at 18 this time.
They adjusted the levels a little, but it still ends (sort of) at L46 and feels incomplete. The rewards are nice, but you probably want to focus on the Grand Company story when you get there rather than the "Main Scenario". They're reworking it, and it will be the main story for 2.0 (with a boss battle, an ending, and all that fun stuff).
2.
I'm mostly just hanging out around Ul'Dah, doing quests I come upon, doing the leve quests from the inn. From what I see you get 4 of these every 12 hours, are these local leves? If so, what are regional leve's and where do I get those / do they count towards this same limit?
Local leves are crafting leves. You get mats from the counter or from the listed NPC, then you equip your tool, hit Synthesize from the Main Menu or click the icon of your craft on the micro menu (bottom right). You select Requested Items, select your quest, and the items are loaded into the ingredient list automatically. Select Main Hand and you'll start crafting. From local leves you get gil and mats, with bonus mats for reaching a higher average quality (100 for first reward, 300 for second reward).
Regional leves are everything else, both battle and gathering, which it sounds like you're already doing. These also include Faction Leves, which are special and cost Faction Credits, earned through regional leves, in order to participate.
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4.
Are there still behests at camps? If so, which camps do they start at and at what time interval? I have not seen any yet, still doing camp Drybone @ +9 right now.
Behests happen, as Eekiki said, every 30 minutes, and are offered at any camp that has normal leves, so for Thanalan that's Camp Black Brush (1+), Camp Dry Bone (10+), Camp Horizon (20+), Nanawa Mines, Nophica's Wells (both 30+), Halatali, and Camp Broken Water (both 40+).
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6.
Crafting used to suck, well I thought it did, you nearly had to level every single profession to craft anything. I want to make some arrows and maybe bows for my archer (bard in the future), I took up woodworking and have a saw, but no recipes. Is there a site with all recipes, or can I buy recipe books from somewhere? What other professions do I need to just make arrows and bows?
In addition to the Lodestone,
mooglebox and
mozk-tabetai are both great for finding items and their recipes. MB also has a gathering tool and mob locator, with bestiary in-progress. Bows are mostly made by Carpenters (CRP), with some upgrades done by others. Arrows are all CRP. You could make some money by selling items you make with the wood you gather to NPCs or on the markets.