Photographers & Film Directors

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Since I cannot answer the questions directly, what I will do instead is take each question, one by one, and give you a general outline (with data and source) that will lead you to craft your own answer.

What is the labor force participation rate? What was the labor force participation rate in 2008? How has it changed since 2008 and what does this change imply for the state of the economy? Does the labor force participation rate effect the unemployment rates reported in the media?

http://data.bls.gov/timeseries/LNS11300000

The LFPR is a very large and broad ratio that computes the number of working age people that are actually working (or looking for work) in any given society. So in 2008, that percentage varied (according to the month) between 65.8% and 66.2%.

Since 2008, this figure has gone down a bit. By the middle of 2012, it had fallen to 63.5% at its lowest. This may well mean that a) there are more working age people in the country now (immigration, etc), and, b) that the economy has not recovered, the percentage working has fallen. If consumption is down, then it makes sense that this basic ratio will go down as the economy shows no sign of improvement.

This is a difficult measure. It gets some media attention, but not nearly as much as the U1 rate reports. One reason it gets the attention it does is that it shows, quite possibly, how many workers have just given up - not looking for work anymore. It might reflect other things like getting paid under the table or going on disability.

How is unemployment measured and reported?

Here is your answer: http://www.bls.gov/lau/stalt.htm
There are 6 measures of unemployment. The problem is that media almost always only report U1 (have to be out of work 15 weeks or more). This is the rate that is almost always the lowest.
The remainder brings in more types of workers:
U2 - those who have lost temporary jobs
U3 - total unemployment (not counting military)
U4 - includes discouraged workers.
U5 - includes ...