BE is an auxiliary verb when used with other verb forms to construct a progressive or passive form. In most schools of grammar, when BE used alone (except in short answers, question tags, etc), then it is not an auxiliary verb.
He is in the street can be analysed in exactly the same way as He sits in the street.
IS is not Aux here but a full verb and should be placed under V within the VP. You should not have Aux in this sentence diagram at all. Hope that helps.
I want to add the following: Verb forms like "is" or "have" can either function as grammatical words in English - IS, for example, is used in present progressive forms like " He is eating right now". "Have" has a grammatical function in sentences like "I have managed to get it done". There is no lexical meaning for IS or HAVE in this case. I would call them lexically empty. This is usually the case with respect to Aux.
IS or HAVE can show full lexical meaning in sentences such as these:
(1) John is a student (here IS means something like "equals" or "is equal to", IDENTITY).
(2) John has a car (meaning "John is the owner of a car", POSSESSION).
To get it right in a tree diagram, you need to determine first whether the word in question has full lexical or empty lexical meaning. I know Nepali a bit, and a verb like HO (the same as HAE in Hindi or Urdu) can actually have both occurrences as IS in English. Hope that helps.
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