Could someone who has at least vague idea about all those questions take care of this or at least explain us what we need?
Well, TECHNICALLY; that can be done by dumping all blocks records and their heights (amount) - preferably from the pool OR explorer, into a accessible web address.
TECHNICALLY; if I were to sync blockchain via some RPC api (PHP/C/any other), dump block by block (not sure how to do it 100%, but I was half-way through in one of those experiments I did with wallets and PHP); and then calculate each height (block amount), add up each to get total amount, I can probably get total amount.
I did some research while tryping this, short one, and I can get some data about each block, like block hash. That may prove to be good for this process, going through blocks, reversing the procedure and calculating block amounts X block numbers. But I'd have to look further into it, for sure.
Lucky for you guys, Saul is not just handsome

:p
EDIT: YEP:
1. getblockhash by block ID (number);
2. getblock by block hash
3. getrawtransaction by block TXID
4. decoderawtransaction by HEX output of previous command.
5. get the amount and iterate XXXXX times to calculate totals.
OK; so, I might do it. Tho, it takes a bit of time. Question is, whale, what can you do for the coin?
