Your goal is to convert RFU into product concentration. For this you need to make a standard curve, or otherwise determine the relationship between RFU and [P].

One way to do this would be to obtain the peptide products with their fluorescent tags. Then you would make various mixtures of the the two products (in a 1:1 ratio) with the substrate to match the range of product and substrate concentrations being created in the enzyme reactions, and measure the fluorescence.

A much simpler way would be to add enough of the enzyme to convert all of the substrate to product and measure the overall change in RFU (assuming that the reaction goes to completion). Then you could calculate the proportion of substrate that is converted to product based on the proportion of the total change in fluorescence.

For example, suppose that you start with 1 µM peptide substrate, add enough cathepsin to completely convert it to product in a reasonable amount of time, add the quencher, and measure a change from 100 RFU to 1100 RFU, a change of 1000 RFU/µM. If in the normal reaction you measure 500 RFU after quenching, this corresponds to production of (500 -100) RFU/(1000 RFU/µM)= 0.4 µM product.

Now a word about measuring initial rates. If you just do an endpoint measurement such as you described, you can't be sure you are measuring the initial rate. You have to confirm this by making measurements at various reaction times, then plotting RFU versus time and confirming that the result is a straight line.

You can calculate the Km and Vmax by a standard Michaelis-Menten analysis such as is shown in every introductory biochemistry textbook.

You often can't measure Kd unless the rate of product formation is very slow compared to the association of the substrate with the enzyme (rapid equilibrium). In that case, Kd = Km. Typically, only Km and kcat are measured for single-substrate enzymes. kcat is Vmax/[E]. Rapid kinetics experiments (stopped flow, quenched flow) are usually needed to find out whether the enzyme exhibits rapid equilibrium. These experiments require special equipment.