When Bitcoin gets to a stage where the mined supply is basically 21m (that is, very little remaining btc left to be mined), will Bitcoin still remain a secure network?
The bitcoin network will remain safe when the bitcoins have been mined out, because the mining process will continue even though the miners no longer get block rewards, but they will get incentives from transaction fees, miners will continue to produce new blocks so that miners will continue to validate transactions throughout time.