The switch I want to replace appears to be wired in a series with the fan switch and the fan light switch. When I replaced the sink light switch with the dimmer, it would not come on. The switch has a wire to the top screw and the wire is stripped and looped around the bottom screw. Does the bottom wire that is looped to the other light have to remain a constant loop or can it be cut and attached to the bottom screw?

The wire that loops from one switch to another is the feed supplying power to \to switches. Yes it can be cut and used to feed the dimmer.

Be sure the power is off, dimmers do not like being connected hot.