What does the scale length affect? I only know that guitars with longer scales are better for lower tunings. Is there anything else that is affected by the scale length?

Longer scale length is not ''better'' for lower tunings. Simply many people prefer it for lower tunings because it allows you to keep the string tension relatively normal when tuning down.

Scale length effects the distance between each fret and the string tension. This, in turn, slightly effects the tone. Shorter scale lengths have a warmer tone with softer bass and the strings feel looser. Longer scale lengths do the opposite, obviously.
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The equation for the frequency of vibration is -

For a different scale length tuned to the same frequency, we want f (the fundamental frequency) to work out the same.

Since we are increasing L (the length) and thus decreasing the 1/(2L) term, we need the T/rho term to increase to compensate.

Rho is the mass of the string per unit length - so if you use the same gauge of string, this stays constant. This means that to achieve the same fundamental frequency on a longer scale length, we need more tension.

The reason that a longer scale length is usually preferred for downtuning is that a guitarist will usually want to keep the string tension the same no matter what tuning they're playing in - it's the tension that they're used to. If the tension changes, then their playing will suffer. Especially bends, since they'll either bend too far or not far enough.

So, in order to decrease f (lowering the fundamental frequency - lower tuning) but keep T fairly constant, there are two things we can do. Increase L, or increase rho. Have a longer scale length, or heavier strings.