1) it works! It just depends on the people. We use "onegai shimasu" for people you know just a little bit, you kind of respect him/her, or you think the person seems older than you. Like, classmates, coworkers, or acquaintances. "Onegai itashimasu" is for when you respect someone or the person is higher position compare to you (usually, the person is head of the group). For example, teachers, managers, leader, or something like that.
(onegai suru) < onegai shimasu < onegai itashimasu
2) I tried to think "I can't eat a little bit more" in Japanese, but I couldn't any sentence.^^; But if it's "I can't eat any more", I came up with!xD
"Mou kore ijou taberarenai hodo, onakaga ippai desu."
3) Definitely, you can say that!xD "anatawo shinu hodo sukidesu."also works. But i think this sentence is for a proposal. But if you say in informal, I absolutely i heard a lot of time "shinu hodo (someone/something) ga suki" For example, "shinu hodo kimi ga suki", "shinu hodo nihongo ga suki", "shinu hodo doubutsu ga suki", and etc.!