They don't rule on anything not written down.

and that would bring up and interesting question of recusal. Since the SCOTUS would be in essence ruling on a case affecting itself. If it were to happen and no one recused, I would say the vote would be 6-2 that the president could make the appointment, with Alito & Thomas voting against. 5-2 if Roberts recused himself.

takes a few weeks. They vote "No" as a block.

Rinse, repeat. They only need to do this a couple of times.

and they are trying to intimidate and threaten the President into nominating a "conservative" for the vacancy, in hopes of maintaining their political advantage on the Court. They are playing heavy-handed politics, in my opinion.

Both parties have held up SC nominees for purely political reasons. The Constitution does not give limitations to the Senate's confirmation process.

The court doesn't rule on "political questions" and as correctly noted, there is no timetable for considering a nomination. Finally, Senators have complete discretion to oppose a nomination for any reason or no reason at all.

A suit would have to be filed in Federal District court by someone who has standing to sue. The entire process would take at least two years before it reached the SCOTUS. It's not going to happen in time to affect this appointment.

The President cannot "request" that the Supreme Court take a case. There is a process that must be followed.

They have to wait for someone to file a suit which then travels through the lower court system until it reaches them.

during the presidency of John Tyler.