Do the wheels and tires extending out mess up the aerodynamics?
Yes.
If so, the mather motorsports idea would work better?
Not necessarily. For a given frontal area, longer bodies have better coefficient of drag (CD) due to the extra time turbulent air has to smooth out. Front tires don't hurt CD that much. Also, as I mentioned, lift reduction via splitter and it's high induced drag may be more appropriate than simple air dam designed to reduce turbulence.
Of course, both a smooth surface and high downforce would be nice. In your case, being a street-driven car, don't do any more than you have; you'll get tired of repairing the nose everytime you crunch it on a steep driveway or road hazard. You can't get that Sentra fast enought to generate much downforce, anyway.
The cooling issue comes up for me because the SE-R water pump supposedly cavitates over 6,500 rpm. Air bubbles SUCK at cooling. I did overheat on the track until I installed the Nissan Motorsports radiator fitted to the NX2000. So, again, for your street duty, a splitter is of little benefit since there is a simple, proven cure. The splitter can increase cooling by managing air flow OUT of the engine compartment. Look at how close the engine and exhaust sit to the radiator and then imagine trying to get air out between them. A splitter can partially seal the under-engine area and create faster air under the car. Fast air = low pressure, helping to suck the hot air out of the engine compartment.
Downforce happens because the splitter forces air to go up, like a plane does to a piece of wood, or a razor does to your peach fuzz. Send air over the top that normally goes under and you create a slight vacuum. Force in this case is area * differential pressure (dP). The splitter will be a big flat plate (pretty much) under the car giving lots of surface for suction to act upon. Being a track-only car, I can put that splitter quite close to the ground for higher dP, so that decent downforce can be generated at relative low speeds. Road hazards are of little concern.
I don't understand your last question. Please paint me a painfully clear picture.