Not exactly sure what you are asking so here goes...
###Moving a planet
Moving a planet
You have a few options for moving a planet, but I'm going to suggest gravity assist. Simply put, have a large amount of mass pass by the planet to change its orbit. To move a planet closer to the sun you will need to increase its speed and probably alter its trajectory to prevent from flinging it out of the solar system. This process will take time and a whole bunch of mass. Simply cannibalize a moon (or several) from an outer planet and launch it towards the inner system in pieces on a close pass to the Earth. Done properly, the launched mass will loose velocity and the earth will gain it. Over time this process will move the Earth towards the sun.
Spinning up a planet
###Spinning up a planet Warning may have geological implications
This is a little more challenging because planets have a whole bunch of inertia and halving the length of a day requires adding a bunch of angular momentum. We are also going to need to add a whole bunch of mass too. The mass will need to be launched on a trajectory that passes very close to the target planet and is moving at a speed that would be equivalent to the velocity of a geosynchronous orbit around the planet. As the mass passes by it needs to be caught by an orbital tether. Catching the mass in this manner increases the overall angular momentum of the system without decreasing the rotational velocity of the earth. With mass captured, reel it in and thanks to conservation of angular momentum, the rotation of the earth will increase. Like so:
###Climate
Climate
Depends on several things, if we are sticking with the Earth-Sun system then the Earth will get much hotter since it will receive more the solar energy than it gets now. Probably pretty bad for the majority of life on earth but Antarctica could be a nice place to live at least.
Now, this is assuming nothing is done to alter the Earth. If we are talking moving planets then altering the atmosphere is easy. Removing the greenhouse gasses is one step that could preserve the earth because without them the earth would be very cold.
With a faster rotation expect winds to be very different, again hard to say directly but expect them to be moving faster. The Coriolis Effect will play a much larger part in the weather than it does here on earth. A combination of more winds and higher temp extremes probably will cause superstorms.
Probably still habitable, just much hotter. For example the solar system inner limit may be as low as .5 AU.