What is the minimum level for each item rarity and type?
In Borderlands 1, legendary (orange colour-rarity) items can only spawn at level 16 or higher, if not 15. Same with class mods.
In Borderlands 2, apparently orange weapons can now spawn at any level. Earlier ammo vending machines have no rocket launcher ammo to sell, so I presume that no rocket launchers can be found until a certain level.
What is the minimum level for each item type? (Particularly, Vladof rocket launchers?)
Rarity levels do not have a minimum item level. It is possible to obtain a Level 1 (or even Level 0!) Hornet from Knuckledragger, for example.
Item types, on the other hand, are introduced gradually, to avoid overwhelming the player and make him/her better understand their value and differences. Weapon introduction levels are:
Source: Inside the Box article.
Unfortunately, there's no exact data yet for shields (2? 3?) grenade mods (around 6, first drop from Boom Bewm), relics and class mods (10 or more).