The verb here is Ἐλθέτω (elthetō), meaning "to come", and it is in the imperative form (think "commanding" something). Other ways to render this in English would be statements such as "let it come", "may it come", or, if we wanted to apply the seldom used English subjunctive to capture some nuance, my translation would be:
"[we pray] that Your kingdom come".
We are expressing our desire that it comes (as insightfully noted by Perry Webb, it's a third-person imperative, not second-person--this is comparable to the Spanish "Ojala", wishing God to make something occur without directly commanding anyone). The aorist tense of this verb indicates a one-time action but does not indicate that the action is complete. The timing is not specified.
Of the options provided in the OP, A1 most closely aligns with the Greek text. We are praying that this will happen.
(textkit has a helpful discussion of Greek aorist imperative here)
This is again an aorist imperative in the Greek, same basic idea.
There are theories that the Gospel of Matthew was originally written in Aramaic or Hebrew (though this, by itself, does not tell us in what language the sermon was originally given). The principal supporting evidence is the statements of early Christian historians (there are actually quite a few who tell us Matthew was written in Hebrew), two of which are cited here:
Irenaeus of Lyons:
Matthew also issued a written Gospel among the Hebrews in their own
dialect (Against Heresies 3.1.1)
Origen of Alexandria (one of the top Hebrew scholars of his time):
First to be written was by Matthew, who was once a tax collector but
later an apostle of Jesus Christ, who published it in Hebrew for
Jewish believers (quoted by Eusebius in HE 6.26.4)
What we have to work with is the Greek text--if there were nuance in this statement in Aramaic or Hebrew we are at the mercy (or inspiration) of the translators.
For an argument that Irenaeus, Origen, and others are referring to Hebrew and not Aramaic, Buth & Pierce have recently argued cogently that ἑβραϊστί and related words were never used to refer to Aramaic. (see R. Buth and C. Pierce "Hebraisti in Ancient Texts: Does ἑβραϊστί Ever Mean 'Aramaic'?")
For my own work arguing that the Gospel of Matthew was originally composed in Hebrew, see videos here and here.
The latter half of the second video is an argument that Jesus spoke Aramaic, Hebrew, and Greek. It does not conclusively indicate what language was spoken when the Sermon on the Mount was first given (that would be a much longer post), but focuses on what language was used when the Gospel of Matthew was written.