Can you tie a static rope to a dynamic rope and rappel safely? If we do a big wall, we will have one of each and in the event of rappelling, need to know if this is safe. Also, what about two dynamic ropes of different diameters, say a 10.5mm and 9.8mm?
It is good that you have a goal, because now you have purpose, that is, you want to stay alive. I especially like your goal because you wrote it down, a written goal represents a real commitment. Your goal also fulfills all the basic tenets of a good goal. It is conceivable, controllable and measurable. All too many times I hear of goals, such as I want to cure Dengue Fever! that are just stupidly unrealistic. You don't, however, need to get too safety crazy because the world will end on 2012 when the Mayan calendar runs out after being in play for over 2,000 years. Let's just keep you going until then and let the cards fall where they may after that.
Know that even in the best circumstances, rappelling is never safe and is the number four killer of climbers, experienced and novice alike. Of course, it is conceivable that you can rappel on a static and dynamic cord and survive, but you must know a thing or two about those ropes. A dynamic rope pared with a static rope (and two dynamic ropes of dissimilar diameters such as your 10.5mm and 9.8mm) could, due to their differing rates of stretch and friction, cause the knot joining the ropes to creep at the anchor. Result? The rope ends get uneven and you will hit the end of one before the other, moving rappelling from being the number four killer to the number three killer. Even if you survive, you'll have a hard time gripping the ropes, because one will speed through your hand and the other won't.
To control your goal, i.e., to rappel co-joined static and dynamic ropes (or two dynamic ropes of very different diameters) and live, you must knot the ends of both ropes! Also, place the knot joining the ropes on the same side of the anchor as the dynamic (or smaller diameter) rope. Rigged this way, the knot will jam against the anchor when the ropes attempt to shift, keeping the ends even. Be aware that the knot might pull through the anchor or jam into it and stick, making retrieval difficult.
Now for the measurable part. If, after completing your rappel, you find yourself at a banquet table and Warren Harding passes you a goat-skin bota of Beaujolais, don't fret, you can't attain every goal. Gear Guy has spoken!