I accidentally did a short selling for one of my shares and there may be a penalty incurred with SGX. May I know how likely is this penalty going to happen?

Call your broker and ask if they have shares to lend you. You will have to pay interest on the borrowed shares, but it will be lower than your $1,000 fine.

This depends on what stock is involved here. If its a popular stock with high volume, there will be higher chances that they can buy in for you by due date. So the likelihood of the penalty will depend on the popularity of the stock.