There is an exercise in our English textbook where I should ask the question "have you ever...?" about my partner's experience. The partner should answer using a set of expressions and one of them is 'go ice skating'. There is also a rule we've learnt in the unit we're studying that the verb 'go' has two past participles 'been'/'gone'. Is it correct to ask "Have you ever been ice skating?". Is it still a question in the Present Perfect? I'm confused because the form is the same as for the Present Perfect Continuous. So, how should I ask the question 'have you ever...' about activities usually following the verb 'go' (go ballroom dancing, go BMXing and etc.)?
The present perfect is not the same as present perfect continuous.
Present Perfect: have been
Present Perfect Continuous: have been going
In both cases, "have" marks the present tense and "been" marks the perfect aspect. In the first case, that's the end. In the second case, "going" marks the continuous aspect.
Present perfect question: Have you [ever] gone ice skating?
Present continuous question: Are you going ice skating?
Present perfect continuous question: Have you been going ice skating?
I don't agree that "been" is a past participle of to go. It is the past participle of to be. However, it does carry a very similar meaning in present perfect constructions:
I have been ice skating.
I have gone ice skating.
The meanings seem even more similar when posed in questions:
Have you [ever] been ice skating?
have you [ever] gone ice skating?
Both of these questions use the present perfect construction. Both are sensible. They both expect the same answer. Either one is appropriate.
The formation of a present perfect continuous question is possible:
Have you been going ice skating?
This is a different question, one that involves something like an established habit rather than a single event. It doesn't seem to be relevant to that exercise in your English text, since the adverb "ever" would be a very unlikely addition to this question.
There are always three verbs in a present perfect continuous construction: a finite verb to mark the present tense, a past participle to mark the perfect aspect, and a present participle to mark the continuous aspect. The present perfect construction only needs two: one for tense and one for aspect.
The reason that this confuses you is that "skating" also has an -ing ending. It is, in fact, a present participle. It is not, however, part of the verb phrase. It is external to the construction. Compare these:
Have you ever gone ice skating?
Have you ever gone to McDonald's?
In these two questions, "ice skating" and "to McDonald's" play the same grammatical role in the sentence. Neither one of them is part of its sentence's verb construction. They are both modifiers. Now compare these:
Have you ever been ice skating?
Have you ever been to McDonald's?
Again, the participial phrase "ice skating" and the prepositional phrase "to McDonald's" are modifiers, external to the question's verb construction. At least, the prepositional phrase must be, since it does not contain anything resembling a verb. It is possible to interpret "have been [ice] skating" as a present perfect continuous verb construction.
You are less confused than you thought you were.
The word "ever" interferes with the present perfect continuous interpretation. With "ever", the "ice skating" must be able to represent something like a single event, rather than a continuous action or a habit. The question "have you been ice skating" has a present perfect continuous interpretation. The question "have you ever been ice skating" makes more sense as a present perfect construction without the continuous aspect.
Obviously, you can avoid this ambiguity by using "gone" instead of "been". That's more a question of stylistic choice or personal preference than it is of either correctness or clarity. The question makes the same kind of sense regardless of which verb you choose.
Either "gone" or "been" is acceptable in those sentences and the meanings are almost identical.
We think of the verb phrase as the two words together: "have been", "have gone". They're both present-perfect, asking about the present state of an event having happened at an indefinite or ongoing time in the past.
("gone" is slightly more active, and "been" is slightly more passive, but they're very nearly the same)