During the State of the Union Address, the President sets the whole room on fire on purpose, nearly killing everyone inside. One Secret Service person bravely put the fire out singlehandedly. The next day, Congress unanimously votes to title him "The Most Honorable Defender of the Nation." Also, the Senate starts to work on impeachment proceedings and votes to remove the President from office.
(There are three issues that need to be addressed in this scenario.)
1. The Secret Service person, even though they were brave, cannot be titled "The Most Honorable Defender of the Nation." Article I Section 9 Clause 8 says "Congress cannot grant titles of nobility," along with other things.
2. The Senate can begin to work on impeachment proceedings. Article I Section 3 Clause 6 says that the Senate is in charge of all impeachment proceedings.
3. The President has to be convicted of a crime before he is removed from office (Article II Section 4). This scenario never said he was convicted.
A forty year old immigrant from Russia is considering running for the Senate seat in the upcoming elections. He has lived in the US for twenty years. Is there a problem?
Yes. According to Article I Section 3 Clause 3, he must be a citizen.
The Chief Justice of the US Supreme Court has died unexpectedly, and the President has decided to appoint a random person who he happened to pass by while walking around the block. This person is not educated and cannot even speak fluent English. Is there a problem?
No, there isn't a problem. In Article II Section 2 Clause 2 says that the President can appoint judges, ambassadors, and make treaties. Also, nowhere in the Constitution does it say any specifications for Supreme Court judges.