Learn English – “Have you got familiar with new working environment?” Which tense should i use in this sentence

The observation behind this question is very nice. Use of this locution in indeed limited, to perfect tenses:

1. Present perfect: I have been to London to visit the Queen
2. Past perfect (pluperfect): I had never been to London before you took me
3. Future perfect: I will have been to London by the time you return

You can clearly imagine putting the phrase into other tenses. For instance, by analogy of I have been silly to I am (being) silly, you could form *I am to London, *I am being to London. Similarly, you expect *I was to London (I was silly) and *I will be to London (I will be silly). But none of these are possible.

Note 1. It is wrong to think of to have been as having have as a main verb. If so, one would expect the possibility of the past perfect have had been (comparing to, say, have had it coming), and this is clearly impossible.

Note 2. There is a (rather outmoded English?) idiom to have been, without any destination/location specified. It is a euphemism for going to the toilet. Monty Python made a recurrent joke out of it in a skit based around an Agatha-Christie-style murder (the reluctance to say murdered led to numerous characters asking simply Has he been ... ?, to which the others would answer something like Yes, before lunch).

Because that's how English grammar works. English verbs have three principal parts:

• the infinitive (go)
• the preterite or simple past (went)
• the past participle (gone).

All conjugations of the verb are derived from these three parts. Conjugations can vary based on a host of factors:

• person (first, second, third)
• number (singular, plural)
• tense (past, present, future)
• aspect (simple/unaspected, continuous/progressive, perfective)
• mood (indicative, interrogative, subjunctive, imperative)
• modality (possibility, necessity, volition, prediction)
• voice (active, passive)

...and probably a bunch of others I'm forgetting at the moment. Despite this plethora of possible conjugations, though, they all derive from these principal parts.

For instance, to generate the progressive aspect, we add -ing to the infinitive (thus, going) and use it with the helper/auxiliary verb to be; to generate the perfective aspect, we use the past participle along with the auxiliary to have.

And for the conjugations you're asking about, the present unaspected indicative active a.k.a. simple present, and the past unaspected indicative active a.k.a. preterite or simple past, well, they are formed using the infinitive and the preterite respectively. Of these two, the present is marked only for third person singular with the -s ending (I go but she goes, you cry but he cries); the past does not vary for person or number (We went, he went). They don't take auxiliaries because that is the rule that governs their formation.

The "positive" (I take it you mean affirmative) is a red herring. The rule for negation in English is simple: put not after the first component of the entire verb construct, whether simple or compound:

I had gone, I had not gone.
She will be going, she will not be going.

Even with simple constructions, this results in perfectly grammatical sentences:

He goes, he goes not.
You went, you went not.

It's just that those sentences are archaic or poetic; modern English replaces the simple constructions with the emphatic modal for the negative:

I go, I do go, I do not go.
They went, they did go, they did not go.

Asking why English follows those rules is a metaphysical question. It's like asking why English doesn't have a dual number or a middle voice: it just doesn't. The language doesn't work that way. So the only possible answer to your question is: those particular conjugations don't need auxiliaries because English grammar is the way it is; English verbs are conjugated according to the rules of the language, and those rules are what make English the language that it is.