I would like to duplicate the products on your ecommerce module and add an "add to cart" button to my detail page. possible?

Yes, it is possible by using link like as follows:  

/store?addcart=xxx

Here xxx is your product SKU

Is it possible to create personalised payment methods ("Unicredit PagoOnline")?

Yes. Please open a support ticket with your requirements using https://www.mandeeps.com/services/request-a-quote so we may provide you the quote.