Say I have one (non tor) browser open and visit a site like Gmail, then using a tor browser, use an email services associated with an alias. Using either cookies or some other mechanism could those two accounts become linked?
Websites can detect that you are using Tor because there are lists of every Tor exit node (just compare IP Addresses and voila!) Because Gmail (i.e. Google) knows you are using Tor, they know you are not really the client you say you are. When Google sends you the email about a login from a different location, and you don't reset the password, you are confirming that the login was you.
Cookies are only cross browser if they are Local Share Objects (LSO) (i.e. Flash cookies). If the Tor Browser does not allow Flash, the cookies will not carry over to the browser. Look at your Flash Player settings to see and manage your flash cookies.
I hope this answers your question.
Yes it's possible. One of the simpliest techniques is called Evercookie and it is just one of the "persistent cookies" family. It's based on system-wide stored data, like HTTPS protocol enforcement cookies and so forth.