You can access Presto screens from tablets and smartphones including iPads, iPhones and Android devices. Presto includes a virtual function key keyboard and mobile layouts that can be customized for specific devices.
Yes, all system and third party screens are web enabled. You don't need the source to give screens a web GUI with Presto.
Your IBM i should perform the same whether you are running the Presto or the green screen version of your screens. You can run Presto in batch or interactively. Presto uses advanced web technologies like Ajax to render the screens as quickly as possible. While you can never beat the rendering speed of text-based screens, your users shouldn't notice a performance difference on most screens.