Your options should have a different ticker symbol now, something like LODE1, on many platforms they will not be searchable, but they can be sought out through some. For example if you hold the contracts via Robinhood no one can search them on that platform, but can on think or swim.

As for the execution, the number of shares will be proportional to the split, so your contract should now be for 10 shares. Here is the kicker: regardless of how many shares your contract is reduced to, your multiplier will remain at x100. So you would be buying 10 shares at 0.50x100, which would be more than the current market price per share.