Is there any common language that is used to create Play Station 1 Games? Or how can I find out what programming language is used for one of those games?
I was first party at SCEA when we launched the PS1, and the overwhelming majority of games were written in C, with some time critical bits in assembler. All of the library calls were C as well.
Most PS1 games were probably written in C, with some assembly and possibly some light "C with classes." This isn't a universal truth, necessarily -- for example Crash Bandicoot had a good portion of its gameplay logic built in a LISP variant.
In general, you can only find out what languages were used for a game by asking the developers of that game. However, some technologies leave tell-tale signatures or watermarks of a sort that can help you make educated guesses.
For native languages, certain compilers or linkers may leave signature patterns or whatnot in the final binary (for example a tendency to store static data at a particular address, or a certain pattern of bootstrapping machine code instructions for the binary. On the PC, you can often run tools like Dependency Walker against an executable to see which runtime libraries it links against, and from there make educated guesses about which compiler was used to build it.
Similarly, games build in managed languages will require their runtime environments and usually complain loudly if they aren't found when the program is launched (this complaint is usually accomplished via a small bit of native bootstrap code in the executable, which you could also look for if you were so inclined.
Of course, this information is generally of little practical utility, since it doesn't really help you solve any particular problems related to your own game in most cases.