Me and my simple questions: Can I do this in FPGA?

It complains because it already has fixed_pkg in the ieee library - and you are trying to redefine it. Modelsim is VHDL 2008 compliant. You dont need to add your files to the project in modelsim. If you really have to add it - do not add it to the ieee library.

The error you are getting implies you have the file already compiled into a library from another location.

As for quartus - if it compiles, it means your design got through synthesis and the fitter. Whether the design is any good is for you to decide.

To see if your code works, you either need to simulate it or run it on a board.