Contacted the head of a group I want to join, but she didn't reply. What to do now?
6 days is not a lot of time to wait. After 2-3 weeks I would send a short followup. 

In general, long emails are bad. The advice I try to follow is keep them 3-4 sentences if I don't know the person and they aren't expecting an email from me. Give them the opportunity to either ask for more details or to setup a call.