I've been reading Tae Kim's Guide to Japanese Grammar, and recently stumbled upon the grammar point that explains the use of か in casual speech. The things is, although Tae Kim's explanation about its use seems pretty good, I'm not understanding what it really means in an actual sentences.

The guide has two example sentences:

こんなのをたべるか？
Do you think he/she will really eat something like this/this type of thing?

I'm not really understanding where the "do you think" comes from. Tae Kim said it's used to consider whether something is true or not, but wouldn't it have the same meaning with と思う in the place of か? Or am I making some mistake here?

こんなのは、あるかよ！
Do I look like I would have something like that?!

I actually think this one is a bit ironic, and the か kind of indicates that. If you take it out, it would become something like "You know, I have something like that". If you add a bit of irony to that sentence, it will actually become very next to the translation given by the guide. Still, I'm not sure.

Short story: I'm having trouble understanding what it means while reading and I'm not being able to use it at all in any sentences I create. I would be very grateful if someone could help me with this.

As described in the explanation, both sentences are expressing rhetorical questions and/or sarcasm. Perhaps it's clearer like this:

Do you honestly think [he/she] will really eat this type of thing?

Also as explained in the description, this manner of expression is really blunt verging on rude, so rather than trying to figure out how to use it in the questions you create, I'd suggest avoiding it until you have seen it in use a lot and are comfortable using it around very close friends.

あ、分かりました。

Even though I do know it's a rude expression, I thought it would be better to at least have a general idea of how to use it. I am indeed aware that it shouldn't be used to anyone other than very close friends.

Anyway, thank you very much.