I have a @HTML.ActionLink in my Razor view and I'd like for it to call a Post action method rather than a Get  one. 
Is this possible?
If you want to invoke POST action, put this link inside form which uses POST action, or use ajax version. You can find some more details here.
Yes and no. Normal ActionLinks will be normal links. Either you have to use a form (with method being post of coorse) and have a link sumbit it. Or you could add in a but of javascript and a nice extension.
Have a look at http://dr2ab.wordpress.com/2011/07/25/linkbuttons-in-mvc-razor/
Might be something for you.