"Where do you know to have lunch" is what I put as well. The "know to have" in English can mean any of three things: 1. Something you have learned as the proper thing to do: "You know to help your little brother cross the street." Might be something a parent tells an older sibling---it means that older sibling should know what she is supposed to do.
Something you have learned as the smart thing to do "I know to have an extra flashlight."
Something you are aware of: "Where do you know around here to have lunch." Means "What are the restaurants you are aware of in the neighborhood that are open for lunch."
This is interesting, today I learned. :)
Conclusion: nope, "Hol tudsz ebédelni" doesn't mean that. I don't see anything cognitive about it. Of course you can only answer the given question for locations "you are aware of in the neighborhood that are open for lunch" but the question simply asks about your abilities or more like choices in this case.
Tud as in "to know" can't take an infinitive at all, so it seems to me. You'll need a subordinary clause for something similar.
Tudok úszni - I can swim (ability)
Tudom, hogy kell úszni - I know how to swim (literally something like "I know how one has to swim")
You know to help your little brother cross the street. - Tudod, hogy segítened kell az öcsédnek átkelni az úton. / Megtanultad, hogy segíts az öcsédnek átkelni az úton.
I know to have an extra flashlight. - Megtanultam, hogy legyen nálam egy tartalék elemlámpa.
For your third sentence, welp, I think you simply wouldn't say that in Hungarian at all. For your third sentence
In English, "Know" can refer to both skills ("I know how to cook") or information "I know when this restaurant closes." or "I know that 2 + 2 equals 4."
How would you translate something like "I know the capital of Hungary is Budapest." in Hungarian "Or "She is so young, she does not know her own name." Or "Do you know my favorite color?"
Is this sense of "know" (meaning to be aware of information rather than knowing how to do some task) conveyed by some other word in Hungarian?
Example, if someone asked "Hol van a busz?" And you did not know (i.e., you were not aware of where the busz was) would you not say "Nem tudom" or "Nem tudok" or would you say something else?
I think all of your examples would naturally be translated using tud. "Tudom, hogy Magyarország fővárosa Budapest" "Olyan fiatal, nem tudja a saját nevét" "Tudod, mi a kedvenc színem?"
The last one is actually instructive. Tud, although it pretty much covers "can", doesn't fully cover "to know". Information that you gather by meeting something/someone or recognizing something is not something you would use tud for. Tudni a color would be awkward, "my favourite color" is still just one specific color. You can learn the answer to the question "what's my favourite color" and then you tudod it. :D
And then there are cases where you wouldn't do similar workaround to still use tud. Like knowing someone. You surely can't learn a person, right? You can meet them, recognize them, be familiar with them... and this kind of "to know" is ismer. (Pretty much the same as kennen in German, once you'd get there.) It would be quite overpowered to learn someone, right? But ismer can be used for other kind of knowledge as well, it's more vague than tud.
Let's take an example. I know the way home.
Tudom a hazavezető utat - I know it because I have learnt it, try and test my knowledge! It feels a bit off.
Ismerem a hazavezető utat - I am familiar with the way, trust me, I've come across it a couple of times.
I know the Bible.
Tudom a Bibliát - I know it, perhaps by heart?
Ismerem a Bibliát - Umm, I have come across it for sure... I've heard about it. I could tell you 3 or 4 sentences about it.
For your question, "Nem tudom" it's going to be. "I don't know it" The conjugation implies a definite third person object.
Yes, the "I know your favorite color" example really means "I know what your favorite color is." Or "I know (that) your favorite color is blue."
Lots of time in English there is an implied "that" when people use "know."
I appreciate your time with the examples. thanks again.