Answer 1

Yes. The following methods will remove them:

• The abilities Air Lock and Cloud Nine prevent the effects of weather.
• Defog may remove Fog.
• If the weather was caused by a move, you may wait for the weather to clear.

You may also overwrite weather with a new one by using a Pokemon that introduces a new weather (via Ability or Move), but that doesn't remove weather from the field.

Comments

Also can cancel opposing weather with your own.

Answer 2

Yes do this: Lets say the rain is up summoned by politoad. Then once politoad dies, you can send in lets say.. steelix. Let steelix use the move sandstorm and wait 5 turns until it subsides and there will be no more weather.
Also, Pokemon with air lock and cloud nine will temporarily negate all effects of weather as long as they are in play

Comments

I've reshown this because I don't see why you hid it, it's a valid answer.