If the lady could clearly enunciate the words better in the faster version, it would help. She runs over her words many times.
I understand that "essere" is used when the verb is intransitive, i.e. there is no direct object being done by the verb.
"I eat (a cake, an apple...)" is transitive, because the verb is acting directly on an object, and would take "avere". "I arrive" doesn't have a direct object. If you said "I arrive at the shop", you need a preposition ("at) to make it work, because the verb is intransitive and would take "essere".
(edit: although just because a verb is transitive/intransitive in English doesn't mean it also is in Italian, e.g. cercare)
Yes, essere is used by many intransitive verbs (including many verbs of motion) and all reflexive verbs.
There are some exceptions, such as camminare (to walk), which take avere, but it's a good rule of thumb.
On the other hand, all transitive verbs take avere.
We're here is a more common everyday translation. We have arrived is quite formal.
i agree! we have "come" in another sentence for "arrivato" (I have come from the hotel), so "come" should be accepted here too. This is inconsistent! I have reported.
It was good English in Shakespeare's time and you'll find phrases such as "Lo, I am come." in some translations of the Bible, but it's not modern English.
So does the ending on the participle describe the subject or object of the verb?
passato prossimo, do they all take the o,i,a and e depending on gender or singular/plural? seems like it is