Understanding 照相 and 照片

Is the first 照 of the example the short of 照相? Though 照相照片 (take a picture picture) sounds redundant...

No, 照 is not short of 照相, so 照相照片 is wrong.

Or 照照片 is just another way to express 照相? This also seems strange to me as 照 is duplicated

Yes, 照照片 is fine because 照片 is a noun meaning photo and 照 is a verb meaning take;shoot;photogragh.

照相 can be taken as the shorthand of 照相片. 相片 is a noun meaning 照片;photo. So, both 照照片 and 照相片 are correct.

I would say that 照相 is a noun, and should be interpreted as the action to take a picture: 我們去照相 （We go to take pictures.）In this context, you can use 拍照 in lieu of 照相。And it can be separated as a verb and a noun: 我拍了几张照 or 我照了几张相。

To summarize:

• 照片 = (noun) photo
• 照相、拍照 = (noun) the action to take pictures
• 我照了几张相、我拍了几张照
  • 照、拍 = (verb) to take a picture
  • 相、照 = (noun) photo

Furthermore, when the context is clear enough (i.e. talking about taking pictures), you can use independently 照/拍 as a verb:

你照/拍了嗎？ = 你拍照/照相了嗎？

Beware that 照/拍 alone have different meanings, that's why the context should be clear enough to use them alone.