All I can say about your Photoshop question is that Photoshop is commonly used for high resolution, high color images in the games industry, so you have no need to switch to any vector based drawing program.
Practically you could also produce your images with a vector based drawing program like Illustrator but you have to convert the images to bitmaps (for use with Construct 2).
As for the concept of "power of two image sizes" ... this is basically a choice made on performance since divisions and squareroots are pretty quick and easy to calculate (some programmer might correct me or give more insight).
power of two image sizes : 2x2 (not really a size for a "picture"), 4x4, 8x8, 16x16, 32x32, 64x64, 128x128, 256x256, 512x512, 1024x1024, 2048x2048
the last (2048x2048) is pretty extreme since it takes a whole bunch of memory (try to keep it below that)
hope this helps...