If Conquerer's Flail is attached to a creature you control and you activate its equip ability targeting another creature you control, there's no time in between activating that ability and the resolution of that ability during which it's not attached to a creature. Assuming it's your turn, your opponents won't be able to cast spells.

The first ability of Conqueror's Flail constantly updates as the number of colors among permanents you control changes. If the number of colors decreases and the damage that was marked on the equipped creature earlier in the turn is now lethal damage, that creature is destroyed. Similarly, if its toughness becomes 0, that creature is put into its owner's graveyard.

The five colors are white, blue, black, red, and green. Conqueror's Flail can't give a creature more than +5/+5. (Gold, artifact, and colorless aren't colors.)