If I purchase game assets, can it be used for commercial purposes?

That depends on which assets, since each creator can decide that for themselves. I would look on the asset's page to find the license section and read it through, usually somewhere should be written if its free for commercial use or not. If nothing is mentioned about that, i would recommend you to ask the creator personally if they allow it. But if they dont answer for a loooong time, then you should not use it for commercial use to be safe (since no answer means no)