Inactive Tutor answered 04/04/19
Okay. The immeidatge answer to your question is that there is one, and only one, auxility verb in Russian, быть. Unlike English, which has a dizzying array of verb forms, Russian has only this one verb.
Now to the construction you ask about: идти гулять. Fortunately, there's an analogous construction in English: "to go walking" or "to go for a walk." What is at issue is whether this is a goal-oriented activity or not. If you wish to say, "I'm walking to the park," then obviously you say, "Я иду в парк." However, if you are not engaged in goal-oriented acitity, if you're walking for the wak of walking, of exercise of whatever, then you "Я иду гулять/ Я иду-гуляю."
Does that help? Remember that auxiliary verbs are ONLY used to form tenses of verbs.
Inactive Tutor
I think there is a confusion seen in the question itself when a compound verbal predicate is mixed with an auxiliary verb used in the compound nominal predicate (Я иду гулять vs. В лесу было тихо)10/08/19