AMUSING, INTERESTING, OUTRAGEOUS, or PROFOUND

Without free will, true worship cannot exist. (If God is God, he certainly has the right to create us for the sole purpose of worshipping him.)

To your latter points, I agree that we know clearly what evil (a.k.a sin) is—sin is anything apart from God's character (e.g. the fruit of the spirit to start).

However, it's not up to us to "get rid" of evil, that's on God, and that's exactly what he did when he sent his son Jesus to die on the cross as a substitute for the punishment we deserve, and when he rose from the grave he signified that substitution was complete. If we truly accept that fact, then God considers us saved ("redeemed"). And, one day Jesus will come back and eliminate evil once and for all.

As to why God allowed evil to enter the world in the first place, well, that's one of the cornerstone discussions of Christian theology, I can't easily summarize that here. In short, a redeemed world can know God's love and worship him more deeply than a world which was never fallen to begin with. (And again, if God is God, he absolutely has the right to create us—and all of creation—for the sole purpose of bringing him glory.) Here's an excellent article that explains this more fully.