There are two parts to this question (even when you cut out the bonus bits).
- How much energy is stored in the earth's magnetic field (ramp up the magnet)
- How much power to keep that field going (drive current through big loop)
The former is given by the $\frac12 L I^2$ - so we need to estimate the inductance of the coil needed and its current.
A single loop around the equator would have an inductance approximately
$$L = \mu_0 b \log(\frac{b}{a})$$
where b = radius of coil, and a = radius of wire. For a 1 cm thick wire we get
$$L = 4 \pi \cdot 10^{-7} \cdot 6.3 \cdot 10^6 \log(6.3 \cdot 10^8)\\
\approx 160 H$$
Now for a field of 0.5 Gauss, we would need
$$I = \frac{2\pi r B}{\mu_0} = \frac{4\cdot 10^7\cdot 0.5\cdot 10^{-4}}{4\pi\cdot 10^{-7}}1.6GA$$
Wow - Giga amperes. I may have to rethink that 1 cm copper wire... if it has about 0.2 ohms resistance per km (from resistivity of 17 nOhm meter), resistance of the loop is 4 kOhm. So power to keep the current flowing would be about $I^2 R = 1.5 E 22 W$. That's a bit steep. Let's increase the copper wire by 100,000 (making it a 10 square meter section) and drop that to a more reasonable (?) 1.5 E 17 W. Because that thin wire would need 100x more power per second than is used by the USA in a year... With a tip of the hat to @CuriousOne who noticed I had a few zeros missing.
But that's not yet estimating the power to ramp the magnetic field up... because that's given by $\frac12 L I^2$, so from the above requires an energy of
$$W = 0.5 \cdot 160 \cdot (1.6 \cdot 10^9)^2 = 2 \cdot 10^{20} J$$
Interestingly, according to Wolfram alpha that's almost exactly twice the total energy use of the USA per year. Better turn off that air conditioning unit and start saving for Armageddon.
That's a whole lot of power... somewhat more than David Hammen estimated in the similar question. And David knows a thing or two about these things, so I'm hoping he will find this and fix my mistake. You will need a very thick wire (or more turns) to keep the power dissipation to something that can be handled by, say, boiling the ocean. Actually, using the ocean as your conductor might just work - as long as you can prevent the current from short circuiting. Conductivity of sea water is about 20 million times worse than for copper, but suddenly it's not so hard to have a conductor with a cross section of $10 km^2$
Superconductors
The question was asked "how about using superconductors"? Here are a couple of thoughts.
First - superconductors have a critical current density above which they stop working. A typical value is $20 kA/cm^2$. At that value, you need 8 square meters of cross section to carry 1.6 GA (whether you do this as a single turn or multi turn), so the volume of conductor is $4\cdot 10^7 \cdot 8 = 3.2\cdot 10^8 m^3$. And you need to cool that volume of conductor to supercooling temperature (and then keep it there...). Thermodynamics is not your friend, and although heat capacity drops with temperature, the energy needed to get 1 J of heat from 4 K to 300 K is about 100 J (75 for "perfect" heat engine, but who has one of those). So getting that much superconductor might be a problem, and cooling it to liquid helium temperatures would be a big problem too... Oh - and keeping it cool: that would be a problem too.
As for the cost; according to http://large.stanford.edu/courses/2011/ph240/kumar1/docs/62-03.pdf cable carrying 200A costs $20/m. So that's 10 cents per amp-meter. We need 1.6 GA x 40,000 km, which is 6 E 16 amp meter, or a cost of 6 E 15 US dollars. The fact that the US GDP is about 1.6E13 dollars means that this would be 400 years of total economic output - not counting the fact that there is just not that much material available.
I think we need another plan...
PS After thinking about this some more, I have come to the conclusion that I should not have ignored the presence of significant amounts of iron in the core of the earth - this changes the magnetic properties, as we no longer have an "air core" magnet. This probably reduces the steady state current requirements significantly but my EM is rusty when it comes to stored energy for that situation.
