If Ichor Rats's last ability causes each player to have ten poison counters, the game is a draw.

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

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

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

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.

Damage from a source with infect affects planeswalkers normally.

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.