Have you tried going to My Account > Manage Account > My Passes whilst logged in on here and under both the Cinema Pass and Entertainment Pass click on the coloured drop down arrow below both passes to expand the pass information further ?
Also sometimes going to My Bills & Payments may or may not give you some further information.
You asked, "Is there a way in which I can see when these deals are due to end on the website or app?".
I find the only way to keep on eye on my Entertainment and other passes start and end dates is to note them in my electronic diary, which I believe most computers and smartphones have by default. However, if not, then there are cheap e-diaries available from most app stores.