I hope I can answer you correctly. I'll determine which Verb form you should use and the subject
Some of the superpowers I dream of having (includes/include) summoning jack o' lanterns on people's lawns during Halloween and making people burst into the Gangnam style dance.
When Some is used, the prepositional phrase says how the verb will be conjugated, thereby making the verb in 3rd person plural. If it were singular (eg. Some water), it would be singular.
And Of Superpowers is indeed a prepositional phrase, but since it's followed by "Some", it is the subject of the sentence.
The I dream of having is a relative clause. I'll put "that" so that you can see it. Look:
Some of the superpowers that I dream of having. — You see that "I" is conjugating "Dream", therefore it isn't a noun.
Harry, along with Ron and Hermione, (attends/attend) Hogwarts School of Wizardry.
According to the site I'll leave bellow, "along with + something" doesn't make part of the subject
"When (the head word of) the subject is separated from the verb by expressions starting with words such as along with, as well as, and besides, ignore these expressions when determining whether to use a singular or plural verb: Example: The politician, ~~along with the journalist~~ , is expected tomorrow."
The extent of our universe and those beyond constantly (amazes/amaze) me.
The Extent of our universe and those beyond is the subject, but, remember that prepositional phrases can't be the subjects most of the time? Therefore, the one who is conjugating the verb is The extent
According to Cambridge, prepositional phrases consist of a preposition and the complement, and the preposition is not only followed by a noun, but also a pronoun.
Would you like to come with me please? (preposition + pronoun)
Also, Our is only a determiner, and since there's the noun right after, I believe it is still a prepositional phrase.
Last two:I'll put in Italic the one with the Singular subject and verb and in Bold the one with plural subject and verb
Dreams within a dream that (is/are) spliced and diced up inside another dream (confuses/confuse) me.
I really understand why you're struggling so much with this. These types of sentences can even confuse native speakers.
Let's eliminate the relative clause for now.
Dreams within a dream confuse me.
Do you see that "Dreams" is the subject conjugating "confuse"? And since "within a dream" is a prepositional phrase, it can't be the subject conjugating the main verb "confuse"?
Let's get the relative clause back.
~Dreams~ within a dream that is sliced and diced up inside another dream ~confuse me~
This is where it gets complicated, since the relative clause refers to the "a dream", although it is a prepositional phrase. I think you might be overthinking about it. I believe that prepositional phrases can conjugate a verb if it is a relative clause referring to them. I'll talk about your second example to attempt to illustrate my point.
"The lines for the elevator that normally (carries/carry) just five passengers (was/were) reinstalled; [...]"
Ok, so if "Lines" were the subject conjugating "carry" (which also would be on account of the way the sentence was structured), it wouldn't make much sense, because they can't "carry" people. But it makes sense if it is the elevator, even though it is preceded by a preposition.
[...] because the crowd of fat commuters (was/were) too heavy for it."
Prepositional phrases can't conjugate verbs, except if they're in a relative clause or preceded by "Some,etc," , which aren't the case here. And "Crowd" is a singular noun, hence the verb conjugated that way.
Sorry for kinda "guessing" these two last examples without having any source of information (I couldn't find one, I have learned it through immersion), but it is indeed true, since you can see people saying it all the time. And don't sweat over too much about prepositional phrases, English isn't math, so it does have a lot of exceptions (and even math does too). I hope I helped.
https://awelu.srv.lu.se/grammar-and-words/common-problems-and-how-to-avoid-them/subject-verb-agreement/subjects-containing-along-with-as-well-as-and-besides/#:~:text=When%20(the%20head%20word%20of,journalist%2C%5D%20is%20expected%20tomorrow. — Your second example
https://grammar.yourdictionary.com/sentences/20-rules-of-subject-verb-agreement.html — Rules in general about it.
https://www.google.com/amp/s/dictionary.cambridge.org/amp/british-grammar/prepositional-phrases — Prepositional Phrases in general