Is it possible to see how close you are to getting the next heart

One heater per building is enough. Putting more than one doesn't really change anything

I believe you can only reach (and subsequently see) the 10-heart cut-scenes if you give each marriage candidate a bouquet. Here's a quote from the developer on a thread from Reddit:

wait, you can get to 10 hearts without giving a bouquet? That was the whole reason for the bouquet mechanic... to prevent players from seeing the 10-heart event unless they show their romantic interest in someone. whoops

From his comment at the end, it sounds like it might be possible (via a bug) to see those cut-scenes without the bouquet, but that will likely be fixed in a future update if history serves.

Update: Here's another comment from the developer on this (again, from Reddit):

I think the ability to non-romantically befriend the marriage candidates to 10 is a great idea, the only thing stopping me from doing it is the large amount of work involved. It might happen some day though. Now if only I could get my hands on Maru's cloning device...

Update 2: I spotted this in the change log for the upcoming 1.07 patch (available April 4, 2016):

The last two hearts are now greyed-out for marriage candidates until you give them the bouquet.

That confirms to me that hearts 9 & 10 are indeed unreachable without a bouquet.