Hi,
Falang is working fine on our end with Joomla 3.0.
I would recommend you to contact Falang's support if you have a bug with it that can be fixed easily, especially if it's a SQL error.
Translating the texts of payment and shipping plugins with code modification is potentially possible. The problem is that you will have to edit the code a bit everywhere... In the cart file of the view checkout, in the status file of the view checkout, in the invoice file of the order view, in the show file of the view order, ...
While with Falang, it's handled automatically and much simpler to setup as you can do it directly via the interface.