I don't think we have any counter like that.

About other error, I guess there must be a glitch. Wait for admin's answer.

Yes some polls get old so they are closed as there is a limit which the person fix when submit a poll. Yes there should be some system through which one could keep a track how many polls he/she partcipated in a day but any how that is saved in the system and they automatically award a highest voter of the day. :)

I decided to give the "voter of the day" a try. I voted on some polls. But some of them were giving me messages that the polls are now closed. That's fine. But the polls that I never opened previously were also saying that I voted on it. How's that?
Secondly, can I keep a track on how many polls I voted on a particular day to keep a count?

I decided to give the "voter of the day" a try. I voted on some polls. But some of them were giving me messages that the polls are now closed. That's fine. But the polls that I never opened previously were also saying that I voted on it. How's that?
Secondly, can I keep a track on how many polls I voted on a particular day to keep a count?

Go to Polls section, click My Stuff and then My Votes.

If the poll creator sets a close date, the poll will not accept voting beyond that date. If the poll creator left the closing date empty/default value, you can vote at any time.

Keeping track on the number of polls you have voted is not bad. All of us do so.