See http://italian.about.com/library/fare/blfare110a.htm for some information about the definite article in Italian
Yes, essere is the auxiliary verb that goes with arrivare. Intransitive Verbs Take Essere Simply put, intransitive verbs are those that do not take a direct object. These verbs usually express movement or a state of being. http://italian.about.com/od/verbs/a/italian-verbs-auxiliary.htm
The noun it's associated with. Summer is feminine singular so it's arrivata. Note that this only happens when the auxiliary verb is essere, possibly for reflexive verbs (it's that way in French but I can't remember for sure with Italian) and occasionally for ones where 'avere' is the auxiliary verb if the subject is prior to the auxiliary verb (either as a noun or pronoun). They have arrived would be Loro sono arrivati (or Loro sono arrivate if all of them were women)
Your question more generally stated is: "Why is the auxiliary verb changed from avere to essere - in this instance, we use è instead of ha as the 3rd person singular auxiliary verb going with the past participle arrivata.
When essere is the auxiliary verb, the past participle has to agree in number and gender with the subject of the sentence. See https://www.thoughtco.com/italian-past-participle-2011705 for more information.
Avere is often used with transitive verbs, which can and often do take a direct object that the verb acts on: lui ha preso la borsa = "He has taken the bag".
In general, essere is used:
1. as the auxiliary for reflexive verbs (which take the reflexive pronoun, see below)
2. for verbs of motion (including staying in place), like arrivare, andare, venire, etc.
3. in idiomatic verb conjugations (which you just have to remember - sorry, no examples there)
Sometimes, verbs taking avere are made reflexive, which both changes the auxiliary to essere and changes the meaning. When conjugated with avere, the past participle remains unchanged, but when with essere, the PP must agree in number and gender with the subject:
Example [I'm not certain of the prepositions here.]:
lei ha ricordato a suo marito - she has reminded her husband"
lei si è ricordata di suo marito* - "she has remembered her husband"
lui ha ricordato a sua moglie - he has reminded his wife
lui si è ricordato di sua moglie* - "he has remembered his wife"
le donne hanno ricordato ai loro mariti - "The women reminded their husbands" le donne si sono ricordate dei loro mariti - "The women remembered their husbands"
Comments/corrections/additions very welcome
It's a matter of grammar. In Italian we use two auxillary verbs to construc the present perfect and past perfect tense: Essere and avere. As a rule of thumb you can say that essere is always used with verbs of locomotion and condition. E.g: Lui è andato al museo - He has gone to the museum. But: Lui ha aperto la finestra - He has opened the window. In English, we now only have to have as an auxillary verb, which is why all Italian forms of past- and present perfect are translated with have as the auxillary verbs. English used to use to be as an auxillary verb to, like many other languages, but it has just come out of use. You might know the phrase The Lord is come. This is exactly the case. We still sometimes can find to be as an auxillary verb in the English language: The train is gone. I hope this helps a little!
One thing that I disagree with Duo about is that I think (and Duo doesn't) that in some instances it is perfectly good English to translate essere to "to be" when used as an auxiliary.
For example, lei è andata - "She has gone" in Duo, but I think that it is also valid to translate it as "She is gone".
When a past participle is used more like an adjective or can be interpreted it that way, in many cases, it is perfectly valid English to use a conjugation of "to be". That is not always true, so perhaps that's why Duo disallows this usage - but Duo is not always correct in doing so.
Use of "to be" as an auxiliary changes the connotation and nuance of the verb, often given it an emphasis or immediacy lacking in the use of "to have".
Example: "She has come" vs. "She is come." The latter usage is somewhat more stylized and might be considered archaic (antique) - but it is a valid usage.
I'd say "she is come" is definitely archaic, but you still come across it in some translations of the Bible, e.g. "Lo, I am come." I might use it if I wanted that association. In everyday conversation we just reduce it to "She's come" and the problem disappears.
Is there an equivalent archaic form in Italian?
I understand the translation, but wht must we translate from aitalian to poor English. While I am struggling to learn Italisn gramar, ehich was mising from the dialevt learned from my Nonna, I deginitely have anecvellent graspbof aenglish gramar, being a retired English teacher. So, again, why use poor English grammar?
That's because modern English doesn't use the verb to be for formulating the past and present perfect tenses. It has simply come out of use. The point of this lesson here is to understand the present perfect and that it's formed with two verbs in Italian, while English only knows one. Grammar can rarely be translated literally without sounding weird.