A. No, there is no need for you to stay logged in any longer for all the emails to be sent. As long as you reached the page saying how many emails are in the que the que will process on it's own without you being logged in.
A. ~membership~ = Title of the Member's Membership
~password~ = Member's Password
~username~ = Member's Username
~fname~ = Member's First Name
~lname~ = Member's Last Name
~email~ = Member's Email
~phone~ = Member's Phone
~siteurl~ = The domain name of the site
~burl~ = The domain name of the site with /admin added to it (DEPRECATED)
~address~ = Member's Address
~city~ = Member's City
~state~ = Member's State
~zipcode~ = Member's Zipcode
~ip~ = Member's IP
A. ~membership~ = Title of the Member's Membership
~siteurl~ = The domain name of the site
~fname~ = Member's First Name
~lname~ = Member's Last Name
~email~ = Member's Email
~phone~ = Member's Phone
~username~ = Member's Username
~parentfirstname~ = Parent's First Name (5.0+)
~parentlastname~ = Parent's Last Name (5.0+)
~afname~ = Parent's First Name (DEPRECATED)
~alname~ = Parent's Last Name (DEPRECATED)
~sitetitle~ = The title of the site (system)
A. ~membership~ = Title of the Member's Membership
~password~ = Member's Password
~username~ = Member's Username
~fname~ = Member's First Name
~email~ = Member's Email
~url~ = Member's Redirect URL
~ip~ = Member's IP (5.0+)
~parentusername~ = Parent's Username
~parentphone~ = Parent's Phone
~parentemail~ = Parent's Email
~parentlastname~ = Parent's Last Name
~parentfirstname~ = Parent's First Name
~surl~ = The domain name of the site (DEPRECATED)
~siteurl~ = The domain name of the site (5.0+)
~burl~ = The domain name of the site with /admin added to it (DEPRECATED)