Question

Can you provide some examples of protists that are unable to move?

(Are these only reserved to photosynthetic protists?)

Answer 1

Flagella developed early in the evolution of eukaryotes, and there are no identified groups of protists which are primitively without flagella.

Explanation:

The picture above shows a heterotrophic euglenid ,Ploeotia , and as you can see on the left side is the anterior flagella and on the right is the posterior flagella.
Flagella or any other element for movement is not only reserved for photosynthetic protists.