Do I really own the logo?
Yes. Every purchase carries a commercial licence: use it on products you sell, in paid advertising, on packaging and signage, for as long as you like, with no attribution. You cannot resell the kit itself as a template.
Can I trademark it?
You can try, and capping sales materially improves your position, but we cannot promise a mark is registrable. That depends on your territory, your sector and prior filings we have no visibility of. If a trademark matters to your business, have an attorney search before filing.
I am a studio buying for a client.
That is fine and it counts as one brand — the licence transfers to your client. A second client needs a second purchase.