That will dictate how many connections anyone has. Give them too much, and assume that certain plots will be resolved way too early, and that others will go nowhere. You just need to make their goals orthogonal to one another, so that they don't interfere. While Richelieu could pursue his political goals, the musketeers could go on adventures, fight duels, woo ladies, etc. etc. Moreover, the high and low needed one another to further their desires.
Plot is the armature upon which character decisions are created.
I can't separate them. Admittedly, I haven't seen how it's going to turn out yet, so take my ideas with a grain of salt. However, we are well along in the writing process and have addressed a number of questions that you have put, and I'll be glad to share our ideas. Most of the ones we've played in were 48 hour LARPs, played at Brandeis University. I've played weekend-long LARP's ranging from 40 to over 100 characters.