if I upgrade GDB, will it affect any other applications in my PC?
No. The debugger is installed in \lazarus\mingw\i386-win32\bin.
You can see the path in Tools>Options>Debugger
$(LazarusDir)\mingw\$(TargetCPU)-$(TargetOS)\bin\gdb.exe
You could place the download of gdb_771.exe in the same folder and change the gdb.exe to gdb_771.exe in that option.
If you download with Internet Explorer you must not forget to "Unblock" the gdb_771.exe (IE always blocks executables during download).
You can right-click the gdb_771.exe and choose properties and check the Unblock option (or button). See attached image.
Because Lazarus uses it's own GDB version in the Windows version it will not effect any other programs. And for your executables... the GDB is only used during debugging in the Lazarus IDE itself.
B.T.W. for normal debugging a program you might not need the Symbols from Libraries so setting the DisableLoadSymbolsForLibraries maybe enough for you. So if you're not debugging in libraries you can just set that option to true.