This is my assumption based on what I know:
Do you need a certain skill to be able to make the respective food/beverage?
All depending on what skill recipe requires, but generally yes, of you have recipe that requires advances skills, skills won't be automatically given to you. so you need to level them or find someone who is proficient
Will the recipe/book be "consumed" as you learn the recipe?
No, you read the recipe from book or scroll and learn it (either immediately or after some time), if you want you can later burn the scroll yourself but it won't be "consumed"
If not consumed, do you have to refer to the recipe/book every time you make that food/drink or you learn it for good the first time you read it?
Again that's what I'm not so sure, it may be that you will know it immediately, may be that you have to successfully follow it few times until your character learns it by heart.
Can we copy or lend the recipe to have someone else learn it as well?
Yes, since recipe will be physically written on something, you can pass it around.
How would copying the recipe work? Can anyone with the skill to read & write do it?
As I understand it will involve scribe skills in order to copy it. But I am not how scribe skills will work, if you need appropriate scribe knowledge to copy more complicated recipes or simply understanding words will be enough. But generally you need original recipe, blank scroll or book, some ink and a scribe to copy it. Maybe if recipe is not complicated you can do it yourself.