Recently i was asked by one of the professor to solve problem in FORTRAN. I am already working with PERL, PYTHON, JAVA, C and C++ but now I am thinking "Is it worth to learn FORTRAN in bioinformatics?" Please suggests.
No. The only Fortran code that is likely to be broadly relevant in bioinformatics is LAPACK, and that has an adequate C interface. Understanding C better is a far better time investment than writing Fortran (though there is a little bit of value in being able to read Fortran).
That depends entirely on what you do. If you are a software developer working on implementation of highest-performance tools that would strongly benefit from fortran go ahead learn it. If this is just a random assignment and you do not plan to make it your workhorse-language, don't. If you are more an analyst than a programmer absolutely don't and spend time on biological background and stats.
As a side note, maybe this is because I am not a native speaker but I find the word "nonsense" in an educated discussion utterly disrespectful as it somewhat implies the writer feels intellectually superior. Just saying.
Yes, it is used, and one will see it more as one moves from pure biology to pure chemistry. Example software whose core is entirely in Fortran: Amber Molecular Dynamics, which runs on both GPU and CPU. That said, if you want to learn Fortran, do not start with FORTRAN77, start with modern Fortran 2018, which is a perfectly fine language with all the bells and whistles of Object-oriented programming and more, including native built-in support for parallel shared/distributed memory computing via Coarray Fortran, which can scale your code from your laptop to the largest supercomputers in the world, without a single line of change in your codebase. Also, if somebody gives you advice on Fortran (whether positive or in particular, negative) first ask them how much they know Fortran. If they do not know Fortran 2003 or beyond, then move away from them and their advice. A good reference book on Modern Fortran is "Modern Fortran Explained: Incorporating Fortran 2018" by Metcalf et al.