I think if you require an email, you should use a form of option one so that the user only needs to enter it once.
Instead of storing their email in a cookie, you could use a session cookie. Session cookies are signed by the server, which means that the user can't modify it. The session cookie would just confirm that the user has subscribed, it wouldn't ...
I think you'll find that the best strategy to 'persuade' (rather than 'force') users to subscribe is to provide very clear and transparent information about the value of doing this (versus not doing this) rather than anything you can do through the user interface or interaction design.
This is because the users have to make a trade-off between providing you ...
I think I would find it odd if a random website would display an email I typed in an input field a while back. Maybe it would be better to just hide it.
I doubt people would use the "new" link. I, as a user, would just use the old link as long as it works.
Valid option. If it is not too distracting, I don't think users would mind.