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Don't know how low-power mode will affect the code, probably depends on where you put it. (I've never tried low-power). Maybe have a check for no activity for a while? Also, you could add a 5V wall power plug to the arduino (instead of battery).
It is hard to tell without looking at the specifics of the components you are trying to use. I believe that 940nm is okay (that is in the infrared spectrum and there was enough ambient infrared when I tested my sensor to get it to work (a room with incandescent bulbs -- or outdoor light works great). Other than that, I really don't know anything about your sensor. You might have to adjust the sensor resistor to get the sensitivity correct. A potentiometer with the right range (0 - a few hundred K ohms is good) works well for this. It is best to just temporarily wire things up to test it. you can always unsolder/cut the wires and resolder if you are careful.
The sensor that I used is actually a phototransister. The first picture that you show looks a lot like a phototransistor. The second picture is a photo-resistor, which is much different. You could make it work, but you'd have to change the circuit. Also, photo-resistors are quite slow to react to a change in light; several tens of millisecond, while the phototransistor only takes a few microseconds. So, you timer would not be very accurate if you used a photo-resistor.Yes! You could add a starting gate with colored lights, and even sounds. That would be cool!
330K ohms for the sensor resistor. Usually the ground (cathode) is the shorter wire, but it would be best to look at the datasheet for the particular sensor you have (if you can find it). You can also temporarily wire the components together (breadboard, alligator clips, paper clips, whatever) and see which way works. You shouldn't be able to break it, even if you get it backwards -- at least not a photosensor.
Yes, send me the error message. Could be that the newer Arduino versions aren't compatible with this old sketch. I'm good at debugging this type of problem.
Yes,6 lanes is just like make 2 - 3 times more. Although if you are new to electronics it can be frustrating and you might want to build two lanes before trying something more ambitious.
One more point, eventually you will run out of input/output pins on your arduino if you try to scale up too much (you will need 1 input and 1 output per lane). But 6 lanes is fine for most arduino boards (you typically have 14 digital pins plus the 6 analog pins can also be used).