By design and definition.
Every decision they make must be based on cases alleging constitutional violations. They do not, with the exception of impeachment or Treason, try cases as other courts do, To say that the USSC is only a court of law is ridiculous.
Does the USSC have a right to declare any legislation illegal? No.
It cannot rule on internal resolutions or organizational matters. Nor can it decide on any law it wants to. Instead, cases must be brought to it. Thus it is a law court.
Should each branch have independent authority to declare constitutional any law they choose, with the force of law, then the government would be in chaos.
Huh? Presidents veto bills all the time. You are just wrong.
Yes they do however their VETO is does not carry past their term if a different president and congress decide to un-veto it.
give me ONE example of a law that has been ruled unconstitutional by the court that is in effect in ANY local, state or Federal jurisdiction.