Does this sign also mean 'election'?
Yes, the sign for 'vote' is frequently used to mean 'election' as well. The context of your sentence will naturally help the person you are signing with understand whether you are talking about the act of voting or the election event itself.
Can I use this sign for voting in a casual poll?
Absolutely! While the sign visually represents casting a traditional paper ballot, it is used for all types of voting in ASL. You can use it whether you are talking about a formal government election or just a casual group vote on where to eat dinner.
Which hand should be the ballot box?
Your non-dominant hand should always be the stationary ballot box, while your dominant hand acts as the ballot being placed inside. For example, if you are right-handed, your left hand forms the 'O' shape and your right hand does the moving.