When an unblocked Rogue I control attacks, I'd switch it with Sakashima's Student and have it copy a StrinkDrinker Bandit on the board. Say, I also have other attackers that are unblocked. Does Sakashima's Student's copied ability of Stinkdrinker Bandit apply to the other unblocked attackers as well as itself?
No, the Ninjutsu'd Stinkdrinker Bandit's ability will not trigger.
Stinkdrinker Bandit's ability is a triggered ability. When the defending player has decided on his blockers, it triggers for every Rogue that is now unblocked. It will not trigger again during the current combat phase.
If you want to Ninjutsu your Stinkdrinker Bandit with Sakashima's Student, you can only do so after blockers have already been declared because of Ninjutsu's timing restrictions: An unblocked creature is any attacking creature that, after the blockers have been declared, has not been assigned a blocker. By that time, it's too late for the copied Stinkdrinker Bandit to trigger his ability.
For your combo to work, Stinkdrinker Bandit's ability would have to be a static ability and read something like "Attacking and unblocked Rogues you control get +2/+1". In that case, it wouldn't matter when the Stinkdrinker Bandit would enter the battlefield, as long as it's before the end of combat.
No, Sakashima's Student will enter the battlefield after it's too late for its copied ability to trigger.
Stinkdrinker Bandit's ability triggers when blockers are declared, but Sakashima's Student's Ninjutsu ability can only be activated after blockers have already been declared (since a creature only becomes blocked or unblocked after blockers have been declared).
508.3d An ability that reads “Whenever [a creature] attacks and isn’t blocked, . . .” triggers during the declare blockers step, not the declare attackers step. See rule 509.5g.
509.5g An ability that reads “Whenever [a creature] attacks and isn’t blocked, . . .” triggers if no creatures are declared as blockers for that creature. It will trigger even if the creature was never declared as an attacker (for example, if it entered the battlefield attacking). It won’t trigger if the attacking creature is blocked and then all its blockers are removed from combat.
509.1h An attacking creature with one or more creatures declared as blockers for it becomes a blocked creature; one with no creatures declared as blockers for it becomes an unblocked creature. This remains unchanged until the creature is removed from combat, an effect says that it becomes blocked or unblocked, or the combat phase ends, whichever comes first. A creature remains blocked even if all the creatures blocking it are removed from combat.