address abc123 is receiving, made some transactions.
coins are now in a change address abZ321 as shown when you follow abc123's transactions on blockchain.info.
So far so good. You received some bitcoins using an address. Then you spent those bitcoins, and the change was received using another address.
bitcoincore wallet shows correct balance, even tho coins are not in abc123.
Correct. That's because bitcoin addresses are not account numbers. They are more like invoice numbers. The exist as a way to track who paid you, when they paid you, and what they paid you for. After that the bitcoins are under control of your "wallet" because of the private keys that the wallet has. Since your wallet has the private keys that are associated with both bitcoin addresses, it shows a balance of all the bitcoins that are received using either of the addresses.
can i still use abc123 to receive and SEND payments, even tho the coins no longer reside there?
Addresses aren't really used to send payments. They are used to receive payments. If you ran a business, and sold some items to a customer and gave them an invoice number of 12345 so you could track when the invoice was paid, you wouldn't then say that you were spending from invoice 12345 when you bought more supplies. You'd just take all the cash from all the invoices that were paid and put it all in the wallet in your back pocket. Then later, you'd pull some of that cash out of your "wallet" and spend it. You wouldn't track which dollars you were spending came from which invoice.
You CAN re-use the invoice number (sorry, I mean bitcoin address) if you want, but you could also just generate a new invoice number (oops, I mean bitcoin address) for every payment you receive. As long as your bitcoin wallet has the private keys that are associated with each of the addresses, all the bitcoins will be under the control of that wallet.
i also used abZ321 to receive coins by accident, is that a problem in the future??
Much like re-using an invoice number, it might make it a bit confusing for you determine in the future which payment was received for what purpose, but other than that it's just another payment to the wallet. Since the wallet has the private keys, it doesn't really care if you are re-using invoice numbers (I mean bitcoin addresses) or not.
