Actually, I get this question a lot.  There is no way to turn off the pilot light without shutting off the gas to your furnace.  Doing this however, will require that when winter comes, you'll need to call me to come and get your pilot light lit back up and to test your furnace.  Money for me, too much money for you.  It is less expensive to just keep the light lit.

Once a month is ideal, but you don't have to.  Most good filters will last up to three months.  Do not go longer than 3 months when changing a filter.

Yes. You should read your owner's manual. Every time you do your filter you should check your gas connections and flue venting. Safety first.