Egwene is slanting her perceptions and favorably describing Halima, whose behavior and timing is highly suspicious.

The truly suspicious thing about Halima is her association with Delana. Her cover story is laughably thin, yet no one seems to question it. You'd think Egwene and her group would be concerned about spies, especially as they've sent their own to the Tower.

She first claims that there is some sort of moral purpose to the Three Oaths, citing them as a creed or code of behavior that unites the Aes Sedai, and provides the common belief that is the core of their organization.

The sad thing is they actually believe that. The Aes Sedai of the late Third Age have absorbed all their own propaganda, which goes a long way to explaining their arrogance. Projecting an air of infallibility is a useful political and negotiation tool; actually believing themselves infallible is a disaster waiting to happen. As for the Oaths, if they were adopted for any reason other than to reassure an understandably wary post-Breaking populace that Aes Sedai should be tolerated and not killed on sight, I'll eat my hat.

None of these underhanded methods of assistance would be possible if the sisters involved started fighting in defense of the factions they support or pretend to support.

The world is better off for the fact that Aes Sedai don't use the Power in conflicts, though. Look at Seanchan - an entire vast continent held under the control of a single dynasty through weaponized channeling. It wouldn't be Aes Sedai helping armies, the Aes Sedai would be the army. The only one that mattered. A despotism waiting to happen.

The other decision is to arbitrarily open the novice book to anyone who asks.

I do think this was a good decision. The old approach to training, which was to turn away anyone old enough to be able to resist the brainwashing, was a horrific waste of talent and was slowly destroying the Tower. And with the Last Battle just around the corner the Light needs all the channelers it can get. But I don't see why the novices were risked by bringing them to the siege. They have Travelling now: why not set up a training camp somewhere far away and safe?

Thanks to her friends binding a skilled political operative to her cause, Egwene is able to get the vote she wants, and in the grandest tradition of Adolf Hitler and Emperor Palpatine, takes power in the time-honored manner of instigating a crisis to trick a legislative body into giving her dictatorial powers.

I really do wonder how this parallel never occurred to Jordan. Egwene was his favorite. Surely no writer would want their favorite to resemble Adolf Hitler?

why do they simply not depose her and name ANY OTHER candidate?

This puzzles me too. I can only assume it's the sunk cost fallacy, that having been dragged so far down the rabbithole they figure that there's no climbing back out.