I've paid for a software under GPLv3.
Can I redistribute it for free (on GitHub) or even (just for my knowledge) charge for it? With or without any changes.
Yes, you may distribute someone else's GPL-licensed software, modified or unmodified, for free or at cost, even if you originally paid for it. If you received the software under the GPLv3, then your further distribution must also be under the terms of the GPLv3.
Any time you distribute the software, you may charge whatever price you like (or no price). The upstream licensor may not force you to set any particular price nor can they collect any portion of your fee for distribution.
This is addressed in the GPL FAQ, from the point of view of the original distributor who may not collect royalties for downstream distribution:
Does the GPL allow me to require that anyone who receives the software must pay me a fee and/or notify me?
No. In fact, a requirement like that would make the program nonfree. If people have to pay when they get a copy of a program, or if they have to notify anyone in particular, then the program is not free. See the definition of free software.
The GPL is a free software license, and therefore it permits people to use and even redistribute the software without being required to pay anyone a fee for doing so.
You can charge people a fee to get a copy from you. You can't require people to pay you when they get a copy from someone else.