Hello,
Welcome to our Microsoft Q&A platform!
> Does MS accept the UWP app converted from win32 app? or I'd better to develop a new UWP app using c#/c++?
Desktop bridge app is acceptable for Microsoft Store, so you can convert win32 app to UWP app to publish it. But when submitting, you will need to fill in some additional information and the store team will review your submission. After passing the review, the app will show in the store. In addition, From this document, it mentions the Desktop App Converter tool is deprecated. So we recommend that you use the MSIX Packaging Tool instead or create Windows Application Packaging Project in visual studio to convert it.
> Do I need to code sign this app with third party certificate?
No, you don't need to sign this app with third party certificate. About how to package your desktop bridge app and sign it, you can refer to this document.