You'll be fine in English in Tallinn as you would in any other Nordic capital. Fluent younger/tech circles, ok to get by anywhere from food stores to hospitals.
Tänan!
Any recommended local sites for gauging rent prices? What's the common website in Estonia for apartment rentals?
(I did look in Google, but in my experience it's best to ask a local for the defacto leader in rentals)
dittoing these sites.
If the grand-parent wants to be central, try Vanalinn (the old town), Kesklinn (city centre), and Kadriorg.
Also remember that many buildings don't have elevators.
I'm unable to find a more subtle way to ask this, so I'll be blunt. (pardon! :)
How is the English literacy in Estonia and in Tallinn in particular? Of course, if someone expects to live somewhere s/he should be expected to learn the local language and customs, but if you're there for only a month or two then it's challenging.