Is the 'e' at the end of, for example, 'je regardE' pronounced?

The answer is difficult to give definitively in writing. It depends to some extent what the word is followed by. At the end of a sentece, i.e., "Je te regarde." it is pronounced ever so slightly, giving the "d" a distinctive touch. But in "Je regarde mon ouvre." it isn't pronounced at all.

I would love for a native speaker to comment, though.

-- Chris (not a native speaker).

The 'e' is mute and it is not pronounced . All you hear is the 'd' at the end . This is the same for all the forms except the Nous and Vous forms.
So in - je regarde, tu regardes, il/elle/on regarde, ils/elles regardent the ´ regard ' is prononced the same , sounding the ´d' .
I have found as a teacher that it is important to stress this at this stage as some students want to pronounce an ´ é ´ sound which creates problems when you are tackling the perfect tense.
Hope this helps ...

Hi Cécile
Thank you and yes it definitely helps.