You can buy the recipes from a chef based on your crafting level for provisioning plus one other level (either above or below, can't remember exactly)
For the first 3 tiers, the recipes are different based on the ALLIANCE of the character. DC is different than EP which is different from AD.
You can also by all of these (usually for much less) from a guild trader as well.
Recipes that drop are actually still set up by ZONE (which was how it was before 1-Tamriel), so you can get some lower-tier recipes from base game zones
1. There are enough skill points in the game that allow one char to do it all. My main is maxed out on all the skills I need to engage combat, has all skills from legerdemain, thieves guild, DB, psijic, antiquarian, all crafting maxed out etc.. That said, while leveling up I had to pick and choose. If there is a way to level up everything - or even just crafting and combat - at the same time, I haven't figured it out.
2. Level and skill points do NOT affect which recipes we can find/steal. As @tmbrinks said, provisioning level does affect which recipes you can buy from NPC vendors, although I don't remember if that is tied up to how many skill points are put into provisioning.
Do daily writs on alts, and have at least one in each skill bracket. That's how I collected all basic recipes for my main char way back.
Edit: if possible, vary the factions if you want to have all green recipes faster.