If this is just an exercise, your first clause, using the present perfect continuous, is the correct conversion from active to passive and is grammatically correct:
Active: I have been learning English for 5 years
Passive: English has been being learned [by me] for 5 years
As you noted, it sounds awkward, which can happen with the perfect continuous forms ...
The action was not completed. It has been continuing ..
I have been learning English for 5 years.- present perfect continuous tense
English has been being learned for 5 years by me.
I have learned English. - present perfect tense. The action is completed.
English has been learned by me.
Inequality (1) infers.
Inequality (2) infers from the fact that...
It is not correct to say that an inequality or any sort of mathematical concept "infers" something. the usual term is "implies".
Inequality (1) can be inferred.
Inequality (2) can be inferred from the facts that...
The type of the second sentence seems much more common....
"Inequality (1) infers..." would be considered an error in academic publishing (e.g., the Springer–Nature and Elsevier families of journals), including mathematics articles.
(I'll leave aside the question of whether "infer" can ever legitimately, in other contexts, be used to mean "imply" based on historical usage.)
Are there passives without a corresponding active?
There might be. It is difficult to find completely clear examples. Sometimes, the word actually has been used (rarely) in the active voice; sometimes, its unclear whether a form that looks like a past participle is being used in a "verbal" participle construction, or merely a "departicipial&...
It's the normal grammatical definition of the passive voice, in which the object of a transitive verb is made into the subject.
For example, if a sentence in the active is:
I gave my roommate a ride,
the passive would be
My roommate was given a ride by me.
To see what the OED is talking about in that some of the meanings of concern are only used in the ...