SCOTUS Cert Recap: School Prayer, Section 1983, Veterans Benefits, and Habeas Corpus

On Jan. 14, the Supreme Court agreed to hear five cases, which present the following questions:

Does the First Amendment permit a school to bar a coach from praying on the field after games?

Can a plaintiff bring a Section 1983 damages claim based on a police officer’s failure to provide a Miranda warning when the interrogation results in self-incriminating statements used against the suspect at trial? 

When a veteran’s benefits claim is denied based on a regulation later deemed invalid as contrary to the statute’s plain meaning, is the denial based on a “clear and unmistakable error” such that the veteran can challenge the otherwise-final denial?

When, if ever, should a death-row inmate’s as-applied method-of-execution challenge be raised via a habeas petition rather than via a Section 1983 claim, and – if it should be raised in habeas – is such a challenge subject to the bar on successive habeas petitions?

May federal habeas courts use the All Writs Act to order the transportation of state prisoners for reasons other than testifying or for trial, and may such courts allow habeas petitioners to develop new evidence without first determining whether such evidence would be admissible?