Not to fall in local language exacerbation's - incorrect (possessive)
Not to fall in local language exacerbations correct (plural)
We should stop to use the washing machine - incorrect(probably) Has a different leaning.
= On leaving the bathroom, we should all stop to use the machine.
= On leaving the bathroom, we should all stop and use the machine.
We should stop using the washing machine - correct. Use the machine
They just air their jeans from time to time and remove any stains - correct
They just air their jeans from time to time and remove some stains on - "on" incorrect, and "some" strange.
We throw less toxic water in the sewer correct - in
We throw less toxic water by the sewer - correct, but unlikely, it means beside, alongside, adjacent to
Periods, if you like.
Sentences end in a full stop, or question mark, or similar.