1.name the two factors that give federal courts jurisdiction over a case. give an example of each.

2.why do presidents prefer federal judges who tend to agree with their views?

3. how is a case usually heard and decided when it reaches the supreme court?

I answered this similar question a few minutes ago. I can only provide the first 2 answers.

2 factors that give Federal Courts jurisdiction over a case.
1) Cases that arise under a Federal Law. (Federal Antitrust law, Patents, Federal Civil Rights law)
2) Cases involving parties that has complete diverse citizenship. Parties or defendants are citizens of different states.

I think presidents prefer federal judges who tend to agree with their views to ensure that whatever plans or laws they implement will not be contested or questioned by any of the federal judges.