I can't tell the cultivar since they all share the same species name but if it's supposed to be self fertile it won't need a cross. You may still want to hand pollenate with said pollen as (going from memory) the fruit set numbers are improved and size of fruit can also be improved.

Should I pollinate within the same flower, or just inter-pollinate using anthers from different flowers and rub the pollens on the stigmas of different flowers?

Since it says its self fertile, you shouldn't need to hand pollinate but I always try to cross pollinate my dragonfruit with pollen from a different variety in order to increase the size of the fruit.

The Red fleshed DF taste varies with each variety. I've had some red fleshed DF that were not sweet and with very little flavor. I would say that the majority of the red fleshed varieties taste much better than the white varieties. American Beauty and Halley's Comet are super delicious Red/Magenta fleshed varieties that are self fertile.
Simon

In this case you don't have cross with other flowers to but it's always good to (at least that's what I was told).

I think I might have found the cultivar of yours, if the package photo is right, it looks like it might be a natural mystic (it had a low density of seeds like yours).

Here is a link that might be useful: Pine Island

We'll see when I harvest, hopefully.

Newgen
My cousin purchased his few yars ago...It is self fertile but not productive as the common white.
good luck with them flowers.
David

It should be able to produce fruit with just one flower but would do better with more pollen from other flowers. If I have multiple blooms at one time I cross them all with each other for help.

good luck,
-Ethan