Here's what your guy would have to do:
manipulate time and space
Well, actually, we all do this, because we all have mass and therefore all exert a gravitational force. But to manipulate things at will, he'll either have to:
- Create new mass and/or energy at a given point. We've had questions similar to this before; unfortunately, I can't find any at the moment. But he'd essentially have to go against the law of conservation of mass/energy to do this, so this approach is a big no-no.
- Manipulate the universal scale factor. Doing this would change the expansion/contraction/overall evolution of the universe. This is also patently impossible.
To do this, he'll have to compress a chunk of matter into an area smaller than the matter's Schwarzschild radius. The process is possible, and it happens during supernovae. However, I highly doubt that a human - no matter what realistic powers s/he may have - would be capable of such a feat.
Now we're breaking special relativity, too! Moving from one place to another instantaneously is also impossible, because you'd be going faster - a lot faster - than $c$. There are many iffy solutions to this, such as using wormholes, but at the moment, they're entirely theoretical. You also have the risk that the wormhole would close up before you can enter it - and this indeed happens in some wormhole solutions.
We've had some related questions here, such as this one. Possible solutions suggested included exchanging matter with the shapeshifter's surroundings, changing the density of the shapeshifter, and (my favorite) having the shapeshifter me composed of tiny nanobots, which can easily change from one form the another. Choose at will.
You're going to have to be more specific on this one. Technically, we're constantly manipulating matter.
Easy. Deflect the light around him. You could do this via gravitational lensing by putting two black holes (or other sufficiently massive objects) on either side of him, so the light is bent away. This has the disadvantage of being a) Implausible and b) Deadly. He'll be stretched to smithereens within seconds.
through solid matter
I seem to recall a question on Physics about this. He'd have to overcome the electric force from the protons and electrons inside the matter, which would be incredibly hard. He'd also have to manage to disassemble himself to fit through any "gaps" between atoms/molecule. I'd say that - once again - this is scientifically impossible.
I have no idea what you're talking about here.
Not to burst your bubble, but all of these things are absolutely impossible.