Here is the sentence I am working with:
Some of the reflection questions included are “What do you think is happening here?”; “How do you think the boy to the right feels? Why?”; and “What should the boy in to right say in this situation?”
OR should it be just commas?
Some of the reflection questions included are “What do you think is happening here?”, “How do you think the boy to the right feels? Why?”, and “What should the boy in to right say in this situation?”
This is a question of style, and different style manuals may give different recommendations. I will be following the Chicago Manual of Style (CMOS). And CMOS says this:
When each item in a list consists of a complete sentence or several sentences, the list is best set vertically.
Note that this does not mean it has to be bulleted. CMOS allows unordered, unbulleted lists as well, like this:
Some of the reflection questions included are as follows:
“What do you think is happening here?”
“How do you think the boy to the right feels? Why?”
“What should the boy in to right say in this situation?”
Note that CMOS also recommends that the introductory text be a complete sentence that ends with a colon, which is why I've rewritten it as above.
If a vertical list is not acceptable…
I suspect you don't want a vertical list of any kind, and also no colon. I doubt that case is explicitly dealt with in any style manual (CMOS is just about the most detailed one, and it doesn't). So then we default to CMOS's general punctuation recommendations, which say the following:
When a question mark or exclamation point appears at the end of a quotation where a comma would normally appear, the comma is omitted. … When, however, the title of a work ends in a question mark or exclamation point, a comma should also appear if the grammar of the sentence would normally call for one. This usage recognizes not only the syntactic independence of titles but also the potential for clearer sentence structure—especially apparent in the final example, where the comma after Help! separates it from the following title. (The occasional awkward result may require rewording.)
“Are you a doctor?” asked Mahmoud.
but
“Are You a Doctor?,” the fifth story in Will You Please Be Quiet, Please?, treats modern love.
All the band’s soundtrack albums—A Hard Day’s Night, Help!, Yellow Submarine, and Magical Mystery Tour—were popular.
Your quoted questions are not titles of works, so they would seem to get no exemption. We would seem to be left with this:
[1] Some of the reflection questions included are “What do you think is happening here?” “How do you think the boy to the right feels? Why?” and “What should the boy in to right say in this situation?”
There is however one overarching precept, which successive editions of CMOS have emphasized in their prefaces and which originally appeared in the very first edition of CMOS:
Rules and regulations such as these, in the nature of the case, cannot be endowed with the fixity of rock-ribbed law. They are meant for the average case, and must be applied with a certain degree of elasticity. … Throughout this book it is assumed that no regulation contained therein is absolutely inviolable. Wherever the peculiar nature of the subject-matter, the desirability of throwing into relief a certain part of the argument, the reasonable preference of a writer, or a typographical contingency suggests a deviation, such deviation may legitimately be made. Each case of this character must largely be decided upon its own merits. (source; also search for 'Rules and regulations' here)
In the spirit of the above, one could argue that in your case, the quoted questions have more in common with titles of works than with reported speech. In particular, they would seem to be significantly 'syntactically independent'. Thus perhaps explicit markers of coordination, such as commas, may be called for. There is of course the temptation to use semi-colons; but CMOS only recommends those when the items being coordinated themselves contain internal commas, which is not the case for you. That would give us this (note that the commas go inside the quote marks):
[2] Some of the reflection questions included are “What do you think is happening here?,” “How do you think the boy to the right feels? Why?,” and “What should the boy in to right say in this situation?”
Conclusion
The only thing that CMOS explicitly recommends about your case is that you don't do it: don't typeset this as a run-in list, but as a vertical one, with or without bullets. If you really must typeset it horizontally (are you really sure you do, though?), then you are somewhat on your own. Both [1] and [2] would seem to be defensible options.
You would use commas as you would with any other list of items.
Whether or not you include a comma before the "and" preceding the last item is up to you. I advise using the Oxford comma.
Some of the reflection questions included are “What do you think is happening here?”, “How do you think the boy to the right feels? Why?”, and “What should the boy in to right say in this situation?”
