"shoutin" is simply "shouting" without the "g". If you see any other "ing" verb without the "g", the same applies. It's written this way to match the way some people pronounce the word.

no shouting = shouting is forbidden no + verb-ing = verb-ing is forbidden Examples: No smoking! No parking! No shouting in the corridor! When giving orders to a group of people we often use "will": There will be no shouting! There will be no cellphones! There will be no cheating!

Yes, you'll sometimes hear or see the "g" dropped from words ending in "-ing". It's a lazy, slangy way of speaking, and makes the speaker sound a little uneducated and/or boorish.

I'm not sure, but I think that "there will no shoutin' " is the same as "We'd better not shout" shoutin'= shouting =gritar. The same happens with runnin'="running"="correr" and touchin'="touching"="tocar"