1) He assumed only a rabba would be sufficiently well versed in Halacha to respect his decision to hold like the Rashba (Brachot 43a) that one must wash one hand before drinking wine. We see Achashverosh held like this opinion, as it says (Esther 1:7):
וְיֵין מַלְכוּת רָב בְּיַד הַמֶּלֶךְ
And the rabbi's wine in the hand of the king.
Did Achashverosh only have one hand? Rather he held of this Rashba.
We see Rabba Vashti held this way as well from her name, which properly pronounced is: Washti, a contraction of Wash and Tea. However, while Washti was strict on herself, she was lenient to others, as it says:
לֹא-עָשְׂתָה, אֶת-מַאֲמַר הַמֶּלֶךְ אֲחַשְׁוֵרוֹשׁ, בְּיַד הַסָּרִיסִים
She didn't follow King Achashverosh's opinion to the hand of the servants
Hence she was killed as a Moredet beMalchut.
2) Esther was a rabba too, as were all the women Achashverosh collected, as it says:
וּבְהִקָּבֵץ נְעָרוֹת רַבּוֹת אֶל-שׁוּשַׁן הַבִּירָה, אֶל-יַד הֵגָי; וַתִּלָּקַח אֶסְתֵּר אֶל-בֵּית הַמֶּלֶךְ, אֶל-יַד הֵגַי
And when maiden rabbot were gathered in Shushan the capital in the care of Hagai, Esther was taken to the kings house to the care of Hagai.
Rabba Esther, who was also a prophetess, certainly was careful about this Halacha. The Torah hints to this in Deut 25:11:
וקרבה אשת האחד להציל את אישה מיד מכהו ושלחה ידה
And the wife of the man (Esther) will come forth to save her husband (Mordochai) from the hand of his oppressor (Haman), and she will send forth her hand.
If Esther was using only one hand to get at Haman at the wine party, it must be because she had washed her other one and didn't want it to touch something impure. (Incidentally, that verse also implies Haman also washed one hand, but that clearly was just to fit in with the king. We know he didn't always hold this way because in 3:9 Haman promises אשקול על ידי עשי המלאכה to pour measured quantities of water on the hands (plural) of his workers.)