Does God have a set day and time when he will bring this wicked world to an end?

Yes, Tracey, He does, but He has told us to always be ready as He will come at a time when we least expect it, as a thief in the night.  He said, "No man knows the day or the hour of His return"  but we can look for signs such as, "As in the days of Noah (and Lot) so shall it be in the days of the coming of the Son of Man" (Luke 17: 25 - 30)

Matthew 24:36 says: “Concerning that day and hour nobody knows, neither the angels of the heavens nor the Son, but only the Father."

No, of course not.  That's a bronze-age story made up to try to impose obedience among the great unwashed.

Yes, God is a God of order within His own Person---everything has a specific place, time and function; God works His will through Divine Order.  Also,  [Matthew 24:36] will clear that up. Yet, this knowledge of the day and hour was withheld from Jesus, the Son of Man, because it was not part of His office, or commission to reveal it to them. 

[Proverbs 16:4] The LORD works out everything to its proper end-- even the wicked for a day of disaster.

Yes.  Let me check my watch.

Yes, and various Protestant churches are constantly "predicting" when that will be. However, Jesus Christ told us that no-one would know the time, so as soon as anyone makes a "prediction", we know it won't happen then.

YES and JESUS made it quite clear not the day and hour but the signs  concerning the end is at hand and they can clearly be seen unfolding now.

Yes, it is all apart of God's plan. 

No, He doesn't have a day on his calendar to end the evil culture that dominates the world.  Why would Jesus tell his followers to pray that the "day comes soon" if it's a set date?

Yes He does, and that day and hour is fast approaching and time is almost up to seek salvation. God will shut the door on gaining salvation just as he shut the door on Noah's Ark and no one else could enter to save their lives.