First Question-Rav Avahu
Soitah daf 40 -talks about Rav Avouhu giving up the chance to be head of the
Learning Academy in order that his colleague who has debts be appointed (&
presumably get money & gifts as head of the academy to pay off his debts).
However this goes against Brochas daf 27b where when they were deciding who to appoint instead of Rabbi Gamliel one of the main criteria required someone who was wealthy so they could travel to Rome, & so someone who would have debts would have been disqualified from being the Head.
Second Question Soitah daf 40 -Agripas
Where they said "You are our brother" to me the reading of the Gemorah is not of (chanifah) "flattery" but of "consloation" because he, Agripas, was crying and they wanted to console him. To me consolation is the logical
reading ie how do you get that it was flattery.
Also if this was flattery when he cried, why was it not flattery previously
when the Rabbis praised him when that he stood when the Torah came even
though he could have halachically sat?
The two sources you mention corroborate nicely. Since it is important for the Nasi to be rich therefore they would enrich whomever was appointed. R' Yehadah ben Besairah had the added advantage of being rich already.
Sometimes translations are misleading. Chanufah means to lie in order to win favor, therefore it was not Chanufah to praise him for what he did since he showed extra Kavod for the Torah. However it was Chanufah to insinuate that he was eligible to reign when actually he wasn't.
Dz