If BTC is mined and nothing more to mine then I believe a new ICE project will be develop to keep this mining machine working in the future...
No, it's not, after all bitcoins are mined I think bitcoin will still stay active and miners still can earn by mining they can still get earn in transaction fees of all miners are gone the bitcoin transaction will be going to slow down like what happened in the past few days the traffic increase and the transaction are stuck because of higher demand of bitcoin and fewer miners.
We can avoid these issues all together if we switch to something more sustainable like POS instead of relying on POW to validate transactions. I highly doubt transaction fees will cover the expenses of running these miners once all coins are in circulation unless we find a cheaper and faster way of validating transactions.