The bans come on a busy Sunday for the match review committee, which has handed South Sydney's David Fifita a one-game ban for kicking Hudson Young.
Fifita struck the Canberra second-rower in the head as he attempted to regain his footing following a tackle in the Rabbitohs' 32-24 loss on Saturday.
The Souths wrecking ball was not penalised on field, but will miss the round-21 clash with Melbourne if he pleads guilty to grade-two dangerous contact.
In-form Raiders hooker Owen Pattie has also been suspended for a week for making an awkward tackle on Souths forward Keaon Koloamatangi in the same game.
Pattie twisted Koloamatangi to the ground as the Rabbitohs were attacking the tryline in the first half and appeared to apply pressure to his neck.
But Twal will at least breathe easily after being offered a $1800 fine for striking Canterbury forward Jaeman Salmon in the Tigers' 32-0 loss on Saturday night.
One of the game's most widely-respected players, Twal lost his composure after an off-the-ball skirmish with Salmon, who said the pair made up after fulltime.
"It didn't hurt that much. There was a bit of theatrics with it, I guess," Salmon said.
"What happens on the field stays on the field. I'm sure 'Twaly' is a good fella.
"He was probably frustrated. We were up on the scoreboard and tensions were high, I guess. I must've gotten under his skin a bit."
The Tigers' best player this year, halfback Doueihi will sit out next week's clash with Canberra if he accepts an early guilty plea for his high shot on Harry Hayes.
Back-up half Fainu is set to miss that must-win Raiders match and the following game against Parramatta for up-ending Bulldogs enforcer Leo Thompson.
Fainu landed in the sin bin for the tackle, with the Tigers reduced to 11 men when Twal was also sent for 10 minutes.
The 14th-placed Tigers are already relying on a minor miracle to make finals, but their hopes of a first top-eight berth since 2011 could officially be over by the time Fainu and Doueihi return.
The presence of Twal is at least a plus, with coach Benji Marshall noting the much-discussed outburst was out of character for the Tigers' longest-serving active player.
"The thing I love about 'Twalie' is he loves the club, and he's passionate and he cares about the result," he said.
"His frustrations, you don't see that very often from him.
"So it's probably a reflection of a lot of us at the moment in how we're feeling, probably as a club.
"It's tough at the moment because the way we started the season gave us a lot of hope and expectation - we're battling at the moment, which is tough but you've got to ride through it."
