Just in front of your windshield, below the wipers, you will see the cowl fresh air intake grill. It is very easy for leaves and other detritus to get into the fresh air intake duct from there. I once actually had those leaves catch fire running the heater in winter time. Had to disassemble it and clean it all out. No damage, just cleaned it out, problem solved. However, if the burning smell is happening with the A/C, it could be your blower fan motor going out. Check to see if the motor is hot when you smell it. If it is hot the bearings are burning up, and there might possibly be foreign matter stuck in there, like leaves, or a pencil. Solution - replace the blower motor, make sure to feel around inside the housing to see if anything is in there that shouldn't be. I have found paper clips, leaves, paper, pencils, etc. Things can get in there from the fresh air intake cowl or the defroster ducts on the dash and cause friction. You might also check the fan speed resistor, sometimes they will smell when burning out slowly. A factory service manual is your friend for this sort of stuff - it will help you see what is involved in taking it apart, and where things are in there.
Another thing to do is, get the smell happening, then open you hood and walk around the engine, smelling it, to see if you can determine if it's coming from the engine compartment. It is possible, but I doubt it. More likely it is one of the above things. Is acceleration really involved? Are you sure about that? If it is, you could have an oil leak or trans problem, but, once again, I expect the problem is in the above paragraph. If all else fails, find an actual real mechanic (most dealerships don't have any - they just have parts replacers).
Wheel size has no effect whatever on ride quality or road noise. Your stock 17" wheels are perfectly fine, just get better tires. Ask your tire man for the quietest, best riding tire, but do your own research first. Your issue is 100% tire-related, assuming the struts/shocks are good. Smaller wheels would likely cause interference due to brake caliper clearance, even with more offset. Just don't go there. I'm not sure where you got the idea that wheel size was the issue, but it most assuredly is not, and whoever told you this does not know what they are talking about, period.