The name "Arduino" is protected. Everyone can make a "Uno" board, but clones may not have the name "Arduino" on it. That's why I assume that your board is not an official board.
I might have spoken too soon. Is on the backside the text "made in Italy" ? Then it is still a official Arduino board.
The Arduino organization was split a few years ago into two camps. Your board might be made by one of them. Later they got together, so there is just one Arduino organization at the moment.
I called your programmer the "worst possible quality". You don't get more quality by paying more money for the same thing.
Be careful when buying things on Ebay / AliExpress / Amazon. It can work without problems for decades, or it can fail in a few days. There are many counterfeit components. Sometimes not-working modules are dumped for a low price. It's a wild world out there.
For the USBasp stick, you need to do the Zadig thing: https://zadig.akeo.ie/
I'm using linux, but I think you start with the default WinUSB. If that does not work, then search online which one to try next.