'to know' in English is used for two cases - 1. to have knowledge of something, e.g. a fact 2. to be familiar with another person - In Italian, as well as in German and French that I know of, each of these cases has its own word. "I know Johnny" (case 2) "I know that Johnny has a new job"(case 1)
Try looking at http://italian.about.com/library/fare/blfare116a.htm which gives some information on the Direct Object Pronouns.
Possibly. But we haven't gotten to the formal La yet. I've lost track of where this question was I must admit. Basically la conosco is I know her, and La conosco is I know you. But when the La is the first word of the sentence it makes it hard to tell, which is why if it was a La I was doing I'd make it obvious by making it Io La conosco