I think it would be helpful if you posted a specific question.
There are couple of ways to look at this. The difference between conjunction and disjunction is similar to the difference between multiplication and addition. Both * and + are functions of two arguments, but they, obviously, in general return different results for the same arguments. While * and + can be considered as functions of natural numbers, conjunction /\ and disjunction \/ are functions that take and return 0 or 1. In fact, multiplication returns the same result as conjunction on {0, 1}.how do you tell the difference between a disjunction, conjustion, negation, and a biconditional?
Also, you understand the difference between "and" (conjunction) and "or" (disjunction) in the natural language, don't you?
Concerning parentheses, there is an order of operations for functions on {0, 1}, just as there is an order for functions on integers. The usual order is: negation, conjunction, disjunction, implication, biconditional.