Like 食べるか、飲むか。 I’ve never heard it like this, so I’m curious. Since this form is casual, do you just say it like you are asking, or something else?
I’ve only heard か used that way in anime and games to exaggerate the question being asked. In daily speech it’d be far more natural to ask 食べる？ with a rising tone, or say something like 食べるの？ with the の being used to ask for clarification. That being said, there may be some situations that call for it that I’m not aware of, seeing as I don’t live with the language in Japan.
Technically, you can. It is completely grammatically correct to attach か to dictionary/informal verbs, but it is often considered blunt, so it really isn’t done. Instead, question marks are used in text and a questioning tone is used in speech, like in English questions.
It can be pretty blunt, as said, and sometimes can mean things like 知るか which is basically “How should I know? / Who cares?”
However, in quotes and embedded questions this is okay. So 田中さんは「わかるか」って言った is okay.