I have a 2007 v6 mustang and I recently got a Pypes true dual exhaust kit making it, dual exhaust from the stock single exhaust and giving it a much better sound. i can see the mpg I get on the dash and I was used to seeing 16-19 but when I looked it said 13.8. I have had the exhaust for less them a week and sure, I‘m being a little harder on the gas to hear the noise but a loss in mpg is a lot to lose just to be a little harder on the pedal. my hypothesis is that I am losing back pressure/force because the air is coming out two pipes instead of one, but I am no car expert at all. why is this happening? and how can I fix it?
First of all, what you said is correct. A true dual exhaust system will drastically reduce back pressure, but this does not hinder fuel efficiency. In fact, it actually assists fuel efficiency, as the less back pressure translates to less effort the engine has to make to expel waste gases. Theoretically, your car should run better, but your car's computer, the ECU, is still programmed for the stock exhaust. This may cause the slight decrease in fuel efficiency (which in addition to your heavier throttle produces the results you see). The simple solution to this is to have either a Ford Dealership, or a Ford-specialized auto shop find a program to tune your ECU (or reflash the ECU) to accommodate a catback exhaust system.
You have to have a machine to change the tires on a sport bike. While it is possible to do it with tire irons, there is so little room on the rim and a sport bike tire has such a stiff sidewall, that it is extremely difficult to spoon a tire on and off. You will also need to have the equipment to balance the tire. I get my tires changed for 20 bucks a wheel (I take them on/off the bike) at a local motorcycle shop. For that money, I don't have to have any expensive equipment lying around. Older bikes, especially the ones that use tubes in the tires, and dirt bike tires are much easier to change with tire irons.
Back-pressure is the LAST thing you need on a fuel injected car - back pressure is what costs hp and gas mileage, and is not anything to concern yourself with unless you start getting extremely ragged with a cam in an older car - and even that is a problem with excessive scavenging and burning valves. You say you got a true dual exhaust kit; what exactly did you do with the oxygen sensors? If you messed up the signal from the O2 sensors, you have mangled your car's ability to manage the fuel maps - that will not only reduce your mileage, but it will adversely affect both your horsepower and cause mechanical problems (starting with fouling plugs, but it can get worse from there). If the O2 sensors are properly located, the next thing I'd think would be causing an issue would be an exhaust leak somewhere in the system - if there's a leak, again, you will be having an incorrect read from your sensors, which will mis-map the fuel.
I did my research before putting on a cold air intake and cat back exhaust on my car and found I was supposed to get about 2-3 MPG better. Didn't happen. The cause I found was that I drove it harder cause it was fun. And that can honestly cost you 4 MPG. Decreasing the back pressure, which is what dual exhaust does, will increase your horsepower because there is less resistance on the engine. In the same roundabout manner, it may or may not improve gas millage. You may want to have it checked out to see if there is a leak or some other mechanical problem, but my hypothesis would be your driving style. Wait until you fill up and see what your millage is then. You may even want to do it twice and try driving like normal. You SHOULD get the same or better. If not, then have whoever installed it check it out.
take the bike and the tire to your local yamaha dealer and have them change the tire. you do not have the skill or the tools to change a tubeless tire.