Messing With Constants = Breaking Physics Really Fast
I have a degree in physics. Trust me on this—fiddling with Planck's constant, universal gravitation constant, permittivity of free space, etc. have far reaching effects. As I understand it, this deity can take the laws of physics, the actual things that our equations are modeled on, and change them as it divinely wills. The short answer is that messing with these things can cause unforeseen consequences, so take my answers as a small subset of things which can happen.
Planck's constant is fundamentally connected to quantum effects—and thus the effects we see in a human scale! It is common practice in undergraduate QM class to simply scale up masses until it approximates Newtonian mechanics.
Looking at Schrödinger's Equation, and some of the equations derived from it, you can do lots of things, such as knowing the position and velocity of a particle, making photons hit like bullets, teleportation, average radii of atoms, strength of chemical bonds, and in short, just about anything by modifying this constant. Unfortunately, a universal change in this constant would likely result in everything getting destroyed.
Turning On/Off Thermodynamics + Laws of Motion
Infinite energy, perpetual motion, anything could happen. This one is basically a free ticket to do whatever you want.
Speed of Light
Sadly, slowing down the speed of light will not allow other things to exceed it, if Einstein is right. Since the speed of light is the universal speed limit, you can't go faster than it, even if it's going at a snail's pace.
What would happen, though, is that relativistic effects would happen very easily. It would be disorienting, as things are dilating and people disagree when events happen. Humans are not well equipped to handle this sort of experience.
Doing this could:
- Throw planets out of alignment
- Make buildings crumble (under their own weight)
- Quickly form black holes which can very quickly consume everything
- Divert missiles, birds, comets, etc.
Perhaps the easiest, and least destroy-everything-right-now option is just to change the gravitational constant for one individual. They'll notice how heavy or light they are, and that may be enough to show off a little without completely destroying everything! This doesn't rule out, of course, people thinking it's just their mind playing tricks on them.
Altering Charges and Masses
The big change here would be in the magnitudes of forces (and energies) related to atom size. Looking at both Newton's law of Gravitation and Coulomb's law, you can see that an increase in mass (or charge) will result in larger forces. Some important impacts from fiddling with these:
- Bond Length: Longer bond lengths mean that some previously stable molecules may become unstable.
- Orbital Sizes and Transmutation: smaller atom sizes means that electrons could more easily go into the nucleus, resulting in certain types of transmutation for elements.
- Density: altering the mass or volume a thing takes up alters its density. This means some things can float, but also some structures couldn't support themselves or be able to support much more.
Changing how refractive indices work can have some unusual impacts on other things, as you can see by perusing the wikipedia article. Of course, we're not entirely sure if a materials refractive index explains properties of things or if a materials refractive index is explained by properties of things. In any case, messing with this could mean holograms, illusions, and lenses at-will.
Messing with Trig Tables / Functions
If you think math simply describes the world, then messing with these values and functions does nothing. If you think math is inherently in the world, or exists outside of our human minds, then this can mess with the effects of geometry on items. To truly answer this, we really need to determine how math relates to the natural world. Numberphile does a good video outlining this problem.