How many active FOSS projects are there in the market?
If you look at the number of packages that are packaged under the Debian operating system, that should give you a good idea. Packages get ported to work under different kernels. Debian GNU/Linux has the most number of packages as of now. Debian KFreeBSD and Debian GNU/Hurd are fast catching up. Also, looking at the size of number of packages that are in Fedora operating system would give a good idea too. There is bound to be a massive intersection between these two projects. Most probably the distribution specific projects would be exclusive to each of these projects. I mention these two because Ubuntu builds on top of Debian and goes to the market. RedHat Enterprise Linux builds on top of Fedora and goes to the market as well.
There are some things, for example, telephony related software that are not yet packaged under any of these major distributions. But they hit the market as well. I don't know how many such software are out there in telephony applications alone. But you also got to look at how many telephony like application domains are out there, just to make sure you cover good ground.
And then, there are many many experimental projects you would find under Apache's umbrella or Mozilla, Eclipse, etc. These software, if they take off, get packaged and enter the market. If they don't, their idea gets life elsewhere and eventually makes it to the market as well.
What is the dynamic of this metric, is it growing or going down?
I have been looking at the number of packages that Debian ships. It has been growing year after year. Looks like it is not staying or going down. Mind you, it is not like just new packages enter the distribution all the time. Some existing packages leave the distribution and go on to become extinct too. Haven't been looking at Fedora's package set's size, though. Besides, there are these experimental projects that mentioned above that you might be interested in.
How many people in total are taking participation in these projects (contributors)?
If I were you, I would look at every mailing list of Debian, Fedora, and all the major distributions, and, every mailing list of major packages such as glibc, kernel, gcc, gdb, bash, PHP, Python, Perl, Eclipse, Netbeans, Java, and on and on for as many as possible. There are serious full timers, casuals, part timers, one timers working on all of these projects.
How many lines of code per year they are producing?
I don't know how to measure that. Perhaps you would get an idea if you pore through the mailing lists of the projects?
How many languages are used, which are the top 10?
I don't know how to answer this as well. Here is my guess of the top ten, FWIW. Top ten meaning, the ones in which I guess most number of lines of code is getting written.
How many abandoned projects (no changes for, say, a year)?
Looking at a major distribution's history should be helpful. Also, some change names, some merge with others, some de-merge or fork.