1. In other words, your owner's draws and contributions are currently recorded under Assets instead of Equity.
You can simply record the transfers between the business and personal accounts. Make sure to exclude (i.e., do not categorize) personal expenses from your personal card. Any positive (debit) value is technically an owner’s draw, and any negative (credit) value is an owner’s contribution.

Once everything is categorized correctly, you can record a journal entry to move the total of these amounts (positive and negative) to the respective Owner’s Draws and Owner’s Contributions accounts.

I highly recommend setting a cutoff date, disconnecting the personal card, and manually posting future business-related transactions directly to Owner’s Equity accounts instead of relying on bank feeds. The personal card's chart of account should have a zero balance once the journal entry is complete.

2. Yes, just classify the transactions as you normally would.
Again, ensure that any personal expenses from the personal card are excluded.

3. There’s no need to create a dummy account.
Simply select the personal transactions from the personal card and exclude them. These personal expenses should never enter your accounting records.

As mentioned in point 1, the personal card account will essentially function as a clearing account for tracking Owner’s Draws and Owner’s Contributions.