Signal processing vs image processing?
Images are signals, and like any other signal can be processed digitally or in continuous-time. So, yes (1) is correct.

How images differ from, say, an audio stream is that discrete points on an image have a 2-dimensional (x and y) spatial pattern (pixels) that comes into consideration when processing them, while audio is considered to be 1-D, with samples only separated by time.

If a signal is considered to be a vector it has more than one dimension (in a vector signal analyzer, magnitude and phase) and so the DSP algorithm is expanded to deal with that.

So the first part of (2) is correct. The second part about ‘3-D’ is not.

RGB isn’t ‘3-D’. It’s just more bits that define a pixel sample. 3-D with respect to images can mean stereo imaging, or it can mean temporal processing over a range of images to, for example, detect motion.  So it’s important to clarify what you mean when you say ‘3-D image Processing’.

So you could have 3-D stereo images that are processed in sequence to detect motion in 3-D space... so 4 dimensions in that case.