Regarding your first question the (main? or at all maybe) reason might not be grammatical but rather that the Hei is a reference to an aspect of Divine Emanation, the Ima Ilaah ("Supernal Mother" - it's something like the globalized Binah iirc)
Because in Tikunei Zohar 79a (in Tikkun 37) we have:
... to unleash Her children from the Exile; at that time there's many Shofar ministers and Sound ministers and Lightning ministers, of whom it says "And the voices and lightnings and cloud are heavy on the mountain, and voice of Shofar very strong ... Moshe will speak and the-Elkym will answer him in voice" - At that time Moshe will converse with the Shekhinah, behold it's the scripture (Num. 12:8)
פֶּה אֶל פֶּה אֲדַבֶּר בּוֹ,
"Mouth to mouth, I be talking with him" - with "the-ELKYM" which is Ima Ilaah, "answering him in Voice" - which is the Amuda Emtzaita [think Yaakob, kol Yaakob-Tiferet] ("Central Column"), and behold haven't the Tannaim explained it to mean: in Moshe's very voice.
...
למפרק בנהא מן גלותא, בההוא זמנא כמה מארי שופרות ומארי דקלין ומארי דברקים, דאתמר בהון ויהי קולות וברקים וענן כבד אל ההר וקול שופר חזק מאד וכו', משה ידבר והאלהי"ם יעננו בקול, בההוא זמנא משה ימלל בשכינתא, הדא הוא דכתיב (במדבר י"ב) פה אל פה אדבר בו, והאלקי"ם דאיהי אימא עלאה, יעננו בקול דאיהו עמודא דאמצעיתא, והא אוקמוהו מארי מתניתין בקולו של משה:
...
For your second question and in contrast it seems from @DoubleAA comment on the other answer there isn't an "article-type" Hei with Hashem's name as that answer's reference to Jer. 8:19 is where it's an interrogative.
Generally in TZ it's taught Names headed in Hei are "feminine," names headed in Y' or W' are "masculine" and YKW"K being His Merciful Kind (~male) Name blessed be He, and a la "I am Hashem I change not" and Hashem is One etc. you can probably discern and meditate and give praise regarding the razin/supernal secrets hinted in this!