Great question! What you are referring to is "Concentrated Solar Power" (CSP).

There are already power plants in the United States and other parts of the world that use (CSP) to produce energy. CSP plants use mirrors to direct a large amount of sunlight into a small point, which then heats up a liquid. The concentrated sunlight can heat things to over 1000℉, so usually water is not heated directly. Instead, another fluid such as molten salt receives the sunlight, then it exchanges heat with water to make steam. This steam can be used for power generation or distillation to drinking water as you suggested.

No, I have heard of no such attempt, and I'm pretty sure it would not be attempted. If you have parabolic mirrors, then it would be more efficient to focus the mirrors on a set of solar panels instead and generate power that way. There are solar power plants that are designed in this way, by using mirrors to collect light and shine it onto a receiver. I am to understand that even this design is outdated, however, and is being replaced with better technologies.

You can certainly boil sea water using parabolic mirrors and condense the steam to get desalinated drinking water.

Here are some links about using solar power to get steam to run turbines! :
CSP Basics
Solar Thermal Power Plants
CSP Technology

The process you described is called "solar thermal desalination." You focus sunlight using a reflective surface (like your parabolic mirrors) to produce steam from seawater, separating fresh water from salt. A quick internet search reveals that there have been many research and development projects that look at how this process can be translated to an industrial scale. You may be interested in reading the following website.