a) Is it possible to get a secure https connection for webmail?
b) Is Squirellmail the only option or is another package available (or instalable i.e. Horde/Imp or Neomail)
Yes. Try https://webmail.dreamhost.com/. You can also use webmail.your_domain with SSL if you don’t mind “mismatched hostname” warnings.
I think others have run into trouble installing Horde/Imp. Search these forums for posts about it.
If you want useful replies, ask smart questions.