Mjoll has little insight into the Thieves Guild which is why her campaign against them is futile. There is loyalty within the Thieves Guild with one notable exception. I actually stopped using Mjoll as a follower because it seemed mean spirited to be the Guild Master and have her trekking around with me like a clueless fool.
You restore the Trinity as part of the steps towards lifting the curse on the Thieves Guild and restoring Nocturnal's blessing on it. Simply killing Mercer won't do that.
This was extremely frustrating, especially because it's the largest Guild in Skyrim. Thankfully I have mods that change this. Not only do I have them as followers but I can have up to three of them at the same time.
There are none. There is a quest where you have to extort money from people and have the option to beat the up to get them to pay but there is also an option in every case where that can be avoided.
You didn't get the
memo?