Good idea!

Not strange at all. You could buy HEAT in multiple ways:
- directly from the devs
- using escrow of well known exchanges

Because not all available HEAT was sold during ICO, a multplier was applied to those who bought in ICO. For every 1 HEAT bought you were actually given 1.5 HEAT. The devs applied this multiplier before they released the coin and so did all the exchanges that were partners in the presale. Only exception was C-CEX, which because of all the delays decided to let people decide if they want to keep their HEAT or get the BTC back. In a couple of days they will change HEAT IOU for normal HEAT and apply the multiplier, that's why people on C-CEX will get additional coins.

Ok..
If I understand the OP correctly there are 25 million heat to be distributed from the genesis block and another 25 million will be produced over the next 4 years.

How many heat are in existence now, and how many will there be once the coins on c-cex are multiplied?

A updated wallet will be out tomorrow but you can fix the current one by updating the blockchain and tweaking some settings.

How can I be sure my wallet is completely synced up?

As someone who is new to heat, I would not mind that.
All coins attract comments that aren't helpful. I'd prefer a discussion of the coin, rather than hyping or so called "fudding".

Moderated threads on BCT always look sketchy to me, because there's no public record of what the moderator is allowing and what they are deleting.  Most projects with a lot of investors on BCT have unmoderated threads with 200+ pages filled with ~50% crap that no one bothers to go back and read through anyways.

I like BCT as a free speech message board.  People can go to slack or heat forum if they want moderated discussion:
https://heatslack.herokuapp.com/
http://heatledger.net/

WARNING! DON'T JOIN THE SLACK IF YOU WANT FREESPEECH! IF YOU WANT THE TRUTH STAY ON BITCOINTALK! CRITICAL VOICES ARE NOT ALLOWED ON THE SLACK OR THE HEAT FORUM!!
SLACK = HEAT FORUM = FAKE NEWS