Should I thank the professor for forwarding me webinar/seminar invites?
I would suggest not for each of the emails. He probably just has a forwarding list and does this as a matter of course. Since you describe it as happening in a research group, he is probably trying to make sure everyone sees things that might advance the work of the group generally.
However, if you find any of them particularly useful for your own work, thank him for those, individually, and say why.
You could, in fact, return the favor when you see something that works for you and might for others in the group. Send them to the prof. and let him pass them on if he agrees on the value.