Does it not have the sense of "shall" or "should"? -- "Where should I wait for you?"
It does, kinda. It sounds like something you'd drop in a phone call, "Where do we meet up?" Or "Where do you want me to wait for you?" "Hol várlak?" of course directly translates to "Where do I wait for you?" but the meaning differs a little from that pretty redundant English sentence.
I'm not sure if I would translate it with "should", though, because there is a grammatical construction in Hungarian that reflects that better. It's commonly called the "imperative form" and you know it from English in sentences like "Stop here!" or "Let's go!" In Hungarian it takes on a few more roles than voicing orders or suggestions, and you can conjugate the imperative form for all persons. Now, if you conjugate it for the first person singular, it usually takes the meaning of "I should do that", a suggestion to myself.
It doesn't seem like the imperative is taught in this course (shame, really, it's so delightfully mind-numbing to learn), so I'll explain a bit. The imperative is usually formed by putting a -j at the end of the base verb, and then the conjugational suffixes. Those differ slightly from the ones you're used to, but it's not very important here. Without a conjugational suffix, it's referring to the second person singular indefinite: várj - (You should) Wait! Now we just add the -lak suffix (with an additional vowel now because we have more consonants to bridge), and we have várjalak - I should wait for you.
So, I would translate "Where should I wait for you?" as "Hol várjalak?"
"Where am I waiting for you"" is a silly question in English. If the person asking doesn't know, who else would? "Where shall I wait for you?" makes more sense but is not accepted.
Because the grammatical structure for asking that question is different in Hungarian. It would be: "Hol várjalak?". You are basically using the imperative form of the verb. And in Hungarian too "Hol várlak?" sounds funny, you wouldn't use it. I guess in duolingo most of the times the goal is to understand the different structures and be able to use them rather than learn expressions.
How would this phrase be constructed if we wanted to say "where should I wait?"
You can express this with the 1st person singular imperative conjugation: "Hol várjak?"
I knew 'should' or 'shall' would be no good here, but the English translation is very awkward. Not something we'd say in the present tense really. Difficult one to translate literally.
How about using a future tense for the English sentence? "Where am I going to wait for you?" But yes, it's an awkwardly worded question for English. In Hungarian it's fine like that.