Playing coop with friends
Solution 1:
The short answer to your question is no, it is not possible to play the entire campaign in co-op. And this is for several reasons.
First, as you mentioned, you cannot even do co-op until you after you beat the first (second if you count the tutorial) boss. Then you get your soapstone that lets you summon others.
Second, you can only summon other players while you are human and staying human is not always easy. Especially if you are new to the game. Anytime you die you become hollow (non human) again and will have to use an item to become human and play co-op once again. To further complicate this point while you are human other players can enter your world and attack you. If they kill you you will go hollow. Some players that do this are very strong, and build themselves for the sol purpose of pvp.
Third, there are simply some areas of the game that you are not allowed to play co-op in. These are also the areas of the game where pvp is not allowed.
To address your other point. When playing coop you are summoned into your friends world (or they into yours). Any actions you preform will only affect that world. You will share exp (souls). But you will not find any items, only the host will. Furthermore, as a summoned friend you will not be able to heal yourself via flasks, but anytime your host heals you will also be healed. Also anytime you beat a boss you will be pushed back into your own worlds and will require re summoning.
I do not say this to discourage you from getting the game. It is one of my favorites and I highly recommend it. However if you are getting it solely for co-op purposes only you might consider looking elsewhere, or doing extra research to make sure this kind of co-op is for you.