The most natural would probably be:
Can anyone open this file and read it?
Could anyone open this file and read it?
Is anyone able to open this file and read it?
Was anyone able to open this file and read it?
Has anyone been able to open this file and read it?
"Do" is an auxiliary verb, so it is followed by a bare infinitive (e.g. "she does go", "he does find"), but modal verbs (such as "could") lack infinitives and so can't be preceded by any other auxiliary - so "I will can", "I should might", "she did could" are ungrammatical.
If a declarative statement lacks an auxiliary verb, we add the dummy verb "do" before inverting the word order to form a question, i.e.
(Declarative) I opened the file.
(With dummy verb) I did open the file.
(Inverted/Interrogative) Did I open the file?
If a declarative statement includes an auxiliary verb (or "be" as a main verb, or sometimes "have"), then the inversion is performed without adding a dummy verb, so...
(Declarative) I am opening the file.
(Inverted) Am I opening the file?
(Declarative) I can open the file.
(Inverted) Can I open the file?