I guess it all depends how abstracted the process is. Actually using the shapeshifting power could run anywhere from "picture a goal form and let magic work out the details of how to get there" to "exert the mental effort to knowingly modify the precise nucleotides in each individual cell and then selectively propogate them in such a way as to arrive at your desired form". The latter would be basically impossible to use, obviously. The whole spectrum is equally valid, though, depending on the kind of setting we're dealing with. There's no law saying superpowers need to be balanced.
Feeling with the mind is something I have thought of for a bit. You wouldn't be able to tell the object's color, and you probably couldn't read text on paper or a computer screen. But you could also tell exactly what it's texture is like and know what it's shape is from every angle at one.
Know what I'm saying?
I've often thought about this (alien senses) in regards to echolocation. People say bats "see" with echolocation, but that's just sorta the closest analogue we have as humans. It's actually hearing, obviously, just a series of complex sounds they can decode into information. But the information they're getting isn't light and colour, it's
distance. I suspect it's more like having an extremely precise sense of exactly how far everything you're "looking" at is from you at a given moment. Precise to the point that you can hear/feel/sense
textures, like tree bark, or the wingbeats of a moth 20 feet away. It's fills the same role as sight, but it's actually completely unlike any sense we have as humans.
There's such thing as human echolocation but animals are on such a completely different level.
Man, this is the kind of thing that makes me want shapeshifting.