Is it possible to cycle a 2.5 gallon tank intended to house just one betta fish? Never intend to add any more fish.
Or is this tank too small and will require weekly full water change-outs?
The asnwer to both questions is, essentially, Yes.
It will cycle. You *can* keep a betta in it. You should perform frequent water changes (50% once or twice a week) if you do keep a betta in it.
For a 2.5g, I'd recommend cherry shrimp & moss, a couple of nice rocks... Think Iwugami.