The rotation speed is not constant, but the non-uniformity are so small so that it won't change anything for us.

Earth may also stop rotating at some point, but this is not even clear. I mean, there are so many effects involved there (tides) and they may change over time. I really think we are fight for the next hundreds of billions of years. Note that I have no source on this under the hand... The calculations should however exist somewhere (no time to google that for now, sorry).