An unwritten tradition whereby nominations for state-level federal judicial posts are usually not confirmed if they are opposed by a senator of the president's party from the state in which the nominee will serve is called

Senatorial Courtesy.

Explanation:

Based on the information provided within the question it can be said that the term being described is called Senatorial Courtesy. This (like mentioned int he question) is a political custom that describes the tendency that U.S. senators have in voting with other Senate colleagues in order to go against a presidential nominee. Which is what is described in the question.

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the fourth amendment protects:

"the right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."  

so this would mean the denial to search and seizure without warrant or permission.