I understand the mining process in Bitcoin, but my confusion is, Did every block verified mean a new bitcoin has been discovered? and if yes did the miner become the owner of this new bitcoin. Also what happened when all coins discovered, did the chain will stop?
You don't understand the mining processing.
First question : Every block verified mean NOT a new bitcoin has been discovered.
Bitcoin mining is making computers do complex math problems to help run the Bitcoin network, and miners are paid with bitcoin for contributing. Bitcoin mining itself is the process of adding new bitcoin transactions to the blockchain – the public ledger of all bitcoin transactions. A new block of bitcoin transactions is added to blockchain every 10 minutes and has been since bitcoin was created in 2009 by Satoshi Nakamoto. Whenever a new block is added to the blockchain, the bitcoin miner who successfully added the block is awarded newly generated bitcoins AND all the mining fees from people who sent a bitcoin transaction during that 10 minutes. Right now a new block rewards 25 new bitcoins, which is a ton of money. https://bitcoindaily.org/bitcoin-guides/what-is-bitcoin-mining/
Second question :
What happens when all the bitcoins are mined?
The bitcoin inflation rate steadily trends downwards. At the time of writing, more than 3 out of every 4 bitcoins that will ever exist has already been mined, and the annual inflation rate is just 4%. The block reward given to miners is made up of newly-created bitcoins plus transaction fees. As inflation goes to zero miners will obtain an income only from transaction fees which will provide an incentive to keep mining to make transactions irreversible.
Due to deep technical reasons, block space is a scarce commodity, getting a transaction mined can be seen as purchasing a portion of it. By analogy, on average every 10 minutes a fixed amount of land is created and no more, people wanting to make transactions bid for parcels of this land. The sale of this land is what supports the miners even in a zero-inflation regime. The price of this land is set by demand for transactions (because the supply is fixed and known) and the mining difficulty readjusts around this to keep the average interval at 10 minutes. https://en.bitcoin.it/wiki/Controlled_supply#What_happens_when_all_the_bitcoins_are_mined.3F