Yes, the CLEO Trading platform supports the setting of Stop Loss and Take Profit orders as Market or Limit Orders. You can close a position through them.
They can be adjusted in the Order Panel in the Mobile App or the Web version.

Prop Firms themselves decide if to offer this feature to their traders or not.
The fee structure (Maker vs Taker fee) depends on the prop firm. Many set them as on the exchange but it’s best to confirm with them to be certain.