I have heard that Germany is using a lot of solar power. I believe Germany is a relatively cloudy place, how is it that they can still generate power? Can this really be economical?

Source: NREL

It is true that Germany receives less solar energy than many regions of the United States. However, less energy does not mean no energy or that solar energy will never be competitive with other sources. Germany still receives sunlight, although not nearly as much as the southwestern U.S. One still generates energy from solar cells on cloudy days--the amount of energy generated is just reduced under such conditions. Germany is a world leader in energy production. In the 1990s, Germany initiated some policies (largely subsidies) that encouraged the construction of solar energy installations. These subsidies helped make solar energy competitive with other energy sources. These subsidies helped solar energy to make inroads and compete with other energy sources. It is yet to be determined how solar energy would fare once those subsidies are inevitably reduced or eliminated. Whenever one switches from using one technology to another, there are some upfront costs involved in that switch. These subsidies are part of that upfront cost. If the subsidies ceased to exist today, solar energy would be much less competitive, but the solar infrastructure is more of a long-term investment. A surprising amount of the cost of solar is associated with red tape.

Source: http://www.forbes.com/sites/toddwoody/2012/07/05/cut-the-price-of-solar-in-half-by-cutting-red-tape/, note that this is from 2012--I could not find more recent figures

In some regions of the U.S., solar energy is already competitive with other energy sources, just as it is in parts of Germany.

EIA Energy Kids

Check out this informative website about energy by EIA! 

EIA Energy Kids

Since power is typically transmitted as AC (alternating) current over long distances, but solar cells would seem to generate DC (direct) current, do solar farms convert the current from DC to AC first? Alternatively, if panels are installed on a house, can everything remain DC?

Photo from abb.com, original from Edward Csanyi of Electrical Engineering Portal

Solar energy must interface with existing power systems. Alternating current is used for transmission because there are fewer losses because it is very easy to transform between different voltages. Heat is dissipated when large currents heat wires, increasing their resistance. With an AC signal, currents can be kept low by transmitting high-voltage signals, decreasing losses. 

Solar cells do not produce a consistent amount of energy throughout the day. Additionally, they produce little energy at night when one often needs electricity. Consequently, the energy from the solar cell must be either stored in a battery or fed back into the grid. It is more common to feed the energy back into the grid as an AC signal due to existing payment schemes and challenges/costs and safety risks associated with storing large amounts of energy. Since these solar cells are connected to the larger power grid, the DC signal that the solar cells produce must be converted to an AC signal.

Furthermore, since many household appliances are designed to operate with an AC signal, it would not be feasible to completely remove a house from the grid and operate the building on DC energy. Already, since computers run on DC signals, you need an AC to DC converter. If one switched to all DC circuits, one would need DC to AC converters. Since most of what we have now either relies on an AC signal or has an incorporated AC to DC converter, it would be expensive to switch to DC electronics. 

I see people talking about record solar cell efficiencies, but most solar cells on the market only give 10-15 % efficiency. Why is that?

There are a lot of reasons and much of it has to do with cost. To make super efficient solar cells, you need to get rid of reflections, for example. To do this, you need to add extra anti-reflective coatings, which make you have to go through more processing steps, costing money. Furthermore, typically you are actually working with solar modules, which necessarily have lower efficiencies than the most efficient cell in them (due to, for example, empty spaces between cells or conduction losses in the cells, themselves, or wiring). For example, peak solar efficiency is obtained at the maximum power point of what is known as an I-V curve (see image below). If you put several solar cells in series in order to build up a reasonable voltage across the module (~700 mV per cell with current densities ~30 mA/cm^2), it is unlikely that the maximum power point of all these cells will line up perfectly, reducing the module efficiency.

Photo from ChemistryBlog

Already, solar cells have a decent upfront costs. Much of this cost comes from the installation of the modules and the electronics associated with controlling the module or its output. Engineering solar cells is always a balance of cost and performance and one must deal with the complexities of real-life materials and processes.