I am sure there is a quick answer, do the totals in the bitcoin ledger balance to the coins issued?
Are the payments and the receipts balanced in each block?
Quick answers to your doubts:
1.) The total amount is always tally;
2.) No bitcoin is lost between transactions; and
3.) No counterfeit bitcoin exist.
The only "way" to destroy circulating bitcoin is by sending them to the unspent-able so-called BitcoinEater addresses which were generated without private keys.