Hello,
1. If the plugin works well with the default theme, it should work well with our theme as well. Unfortunately, I cannot tell you exactly which plugin will be the best in this situation because I don’t have the information from customers on which is better to use or which plugins they are using.
2. I don’t know what is “Cartflows”. Could you please explain?
3. As for the Custom code, in general, it should work but we cannot provide such code because the “Checkout” page comes from WooCommerce so we cannot influent it.
Kind Regards