1. How did Deputy Attorney General Rod Rosenstein react to President Trump's firing of FBI Director James Comey?
"The Times claims Rosenstein told other officials that he might be able to persuade Attorney General Jeff Sessions and then-secretary of homeland security John Kelly to invoke the 25th Amendment."
2. What does Section 4 of the 25th Amendment give the Cabinet the power to do?  Why would they do this? 
It gives them the power to decide if the president is unfit and they may do this if the president is unable to discharge the powers and duties of his office.

3. What does Congress do if the Cabinet exercises this power?
Congress would need to decide if this can go through, if the president disputes it, and they vote needing a two thirds majority to keep the Vice President in charge. 
4. What happened to the presidency when James Garfield or Woodrow Wilson were unable to fulfill their duties as POTUS?
They "lingered on the presidency" and just let them ride it out since they were still breathing, just less capable.
5. What event finally got Congress to address the problems with presidential succession?
"The chaos and instability that followed John F. Kennedy’s assassination finally spurred Congress to move toward solving these problems. "

6. Besides the powers adressed in #2, what else is covered in the 25th Amendment?

"It provided, finally, for a simple way to fill a vacant vice presidency — the president nominates someone, and both Houses of Congress take a vote."

7. What would have to happen in order for VP Mike Pence to assume power right now?
'The vice president and eight Cabinet secretaries have to do is put in writing that the president is “unable” and send that message to the Speaker of the House and the Senate’s president pro term.'
8. What does "unable to discharge the powers and duties of his office." mean?
There is not a definitive answer to what it means but " it could entail not just physical inability but a judgment call on mental health or even, conceivably, poor character or simple disagreement."

9. What could the president do if he disagrees with his Cabinet?
"If the president does this, he or she would get their powers back in four days — unless the vice president and at least eight Cabinet officials say, in writing, that he is still unable."
10. How does this article differentiate this action from a coup?
It says it can feel like one but it is technically not "because it’s indisputably legal and constitutional."