My Sony a65 has a 24MP and 10MP mode. Will shooting at 10MP result in less image noise? I'm looking to do more night photography.
If they implemented it in hardware as pixel binning it will reduce the noise very efficiently. But that would reduce the MP count by 4, not 2.4, so they are just resizing, which you could do yourself, with more control over the algorithm used. It is more a feature to reduce the file size.
Yes, but don't do it that way. It will take the whole image and re-size it before it is saved to disk. This will reduce the noise, but it is an irreversible operation that can be better done on your computer. Save the RAW file and convert on your computer. If you are not satisfied with the noise consider options such as image stacking.