Will Earth's tides go away as the Moon moves farther away from us?
As explained here, the Moon is slowly moving away from Earth. However, this does not mean that the Moon will ever permanently leave us! Similarly to how tidal interactions between the Earth and the Moon have caused the same side of the Moon to always face Earth (called tidal locking), Earth's rotation period also is gradually slowing down to that point. Scientists predict that it would take 50 billion years for Earth to slow enough to permamently face the Moon, at which point the Moon would stop receding from the Earth and Moon-induced tides on Earth will cease. But 50 billion years is a VERY long time period, especially since the death of our Sun in 5 billion years will likely engulf both Earth and the Moon, or at the very least break them apart!
So in short, yes, over very long time periods the Moon will slow Earth's rotation to the point where there are no tides caused by the Moon, but at that point the Earth-Moon system will no longer exist.