(c) Charges may be subject to the outcome of the matter for which the service is provided, unless a contingency charge is prohibited by subparagraph (d) or other laws. A contingency fee agreement must be signed in writing by the client and indicate the method of determining the fees, including the percentage(s) to which the lawyer is entitled in the event of a settlement, proceeding or appeal; litigation and other costs to be deducted from recovery; and whether these expenses are to be deducted before or after the calculation of the conditional fee. The contract must clearly inform the customer of all costs for which the customer is responsible, whether the customer is the winning party or not. At the end of a contingency fee case, the lawyer must provide the client with a written explanation of the outcome of the case and, if there is a recovery, the referral back to the client and the method of its determination. . . .