For the 1st, you want to pick an email marketing software like Aweber or MailChimp to manage that as well as provide you a widget for your site.
The 2nd, it looks like vCita has plugins that address this:
http://profiles.ww.wp.xz.cn/vcita/
The 3rd, just get social share buttons that have an email button. I think all of them do. Here is one I like to use:
http://ww.wp.xz.cn/plugins/shareaholic/
