Yes, ALL heat sources should be regulated.
No, you can't use any fixture. It has to have ceramic inside rather than plastic.
UTHs are not designed for ambient temps. They are simply there to provide a hot spot to aid in digestion.
In the warm weather months I unplug my UTHs and run ambient temps. In the cooler months, I run both. I haven't turned my UTHs back on yet, but will be within a few weeks.
So, unless the room your snake is in remains in the mid 80s you will need an additional heat source.