A player who has ten or more poison counters loses the game. This is a state-based action.

Infect's effect applies to any damage, not just combat damage.

The -1/-1 counters remain on the creature indefinitely. They're not removed if the creature regenerates or the turn ends.

Damage from a source with infect is damage in all respects. If the source with infect also has lifelink, damage dealt by that source also causes its controller to gain that much life. Damage from a source with infect can be prevented or redirected. Abilities that trigger on damage being dealt will trigger if a source with infect deals damage, if appropriate.

If damage from a source with infect that would be dealt to a player is prevented, that player doesn't get poison counters. If damage from a source with infect that would be dealt to a creature is prevented, that creature doesn't get -1/-1 counters.

Damage from a source with infect affects planeswalkers normally.

Whenever you cast a creature spell with infect, Hand of the Praetors's last ability triggers and goes on the stack on top of it. It will resolve before the creature spell does.

The last ability triggers only if Hand of the Praetors is already on the battlefield at the time you cast a creature spell with infect. Casting Hand of the Praetors itself will not cause its own last ability to trigger.