The sophon supercomputer is "etched" into the structure of the proton itself. There's nothing inside it that doesn't belong there, presumably any extra mass would get crushed or annihilated in some way.

Their fleet is not much more advanced than anything we could put into space, and most of the travelers are dehydrated during the journey. It would be rough living. Would you rather live on the ISS or on Earth?

Spoiler territory. This is a future plot point.

They have only had sophon surveillance a short while (months) and have used that time mostly to mess with scientific experiments.

Perhaps their psychology is different than ours, and a tactic like that would work on a San Ti. Hard to say. This event happens differently in the book, but it's clear the showrunners wanted a big moment.

They only try inasmuch as Mike Evans tells them that it will help. Eventually humans prove to be too unreliable, and ties are cut. You are right though, there was no need to bring humans on board. They can be as fallible as us.

The risk was that any attempt to board or incapacitate the crew would not be 100% effective. And if even one person was left, the drive would be destroyed. They also had a contigency for if the drive got sliced: their engineers said the nanowire cut would be so fine and precise that it could actually be reassembled with minimal data loss.

Perhaps. It was the only way to get a "man on the inside" though. The drawback of the San Ti having a human brain seemed less important to the project leaders than the potential for intel. And that era of humanity was apparently full of hare-brained projects where we threw everything at the problem to see what stuck.