Bitcoins will be mined until much longer than that although the rewards would be very little itself.
It would mostly be transaction fees that the miners would be getting though
In 2140 the coins distribution is over, maybe this is the end of bitcoin miners or maybe much early, because the diff is increased and make a profit from mining is low.
You need a free electric cost and much hash.
Yes but mining is still very, very profitable. The amount of hashpower that we have at the moment is enormous. We could cut this hashpower in half and still have a very secure network.
Also, today in average to secure 1 Bitcoin transaction it costs in electricity as 1.75 household spends for a whole day. This is just a lot of hashpower and it goes to show you that mining is still very lucrative. We don't need to worry about the miners and their future, Bitcoin mechanisms will take care of this as well.
And in 2140, when mining stops, Bitcoin will even be huge and there will be enough transactions for Bitcoin to support itself or Bitcoin will not exist.