First: I am not a lawyer. With that in mind:
Can I use GNU General Public License v3 software (in this specific case the OpenFOAM) to do consultancy?
Yes.
That is also part of the Free Software Foundation's Free Software Definition: The freedom to run the program as you wish, for any purpose (freedom 0). And since the GNU GPL v3 gives you all four freedoms listed there, you are fine to do that.
Do I need a special authorization from Linux (OS) and/or OpenCFD Ltd (owner of the OpenFOAM Trademark) for using their software?
No. You do not need special permission from them to use the software, that is to run the software on your computer(s). However, if "using the software" also includes modification of the source code and subsequent distribution of the modified program to the people you are consulting, you have to make sure they can get the modified source code, too.