These are some great questions. Thanks for raising them. I’m hoping that some of my answers will be helpful, and I’m hoping that this thread will provide me a chance to learn from you and others as well.
To your first question: “how likely is it that the phrase ‘in the name of Jesus Christ’ modifies both verbs,” I think that it is unlikely for three reasons:
First, the NT most commonly connects being baptized with in/into the name: Matt 28:19; Acts 2:38; 8:12, 16; 10:48; 19:5; 22:16; 1 Cor 1:13, 15. I don’t think repenting into the name ever occurs (other than the possible example you point out here).
Second, the change in person, number, and voice that you note between μετανοήσατε (repent!) and βαπτισθήτω (let each of you be baptized) creates a degree of separation between the two clauses. Thus, I think this separation makes it unlikely that Luke meant a preposition from the second clause to apply to both clauses.
Third, if the original text contained the φησίν (Metzger comments: "A majority of the Committee was impressed by the diversity of early testimony supporting reading (b), but preferred to enclose φησίν within square brackets because of the weight of codex B, which lacks the word.), then I think it is even more unlikely that the preposition modifies both verbs. This variant between the two commands would create even more separation between the two clauses.
Now, to your second question: “why is “be baptized” singular?” I’d offer three potential answers.
First, Luke seems to introduce an intentional ordering in these commands. Peter issues the first command (μετανοήσατε/repent) to all of his hearers. The second command applies only to those who obey the first: “All of you need to repent. Then, if one repents, let that person be baptized.”
Second, I would think that the shift from active to passive voice affects the person and number of the second command.
Third, the change in person, number, and voice along with the pronoun ἔκαστος/each one seems to add some level of emphasis or urgency to the second command. Perhaps Luke highlights the focus in Peter’s speech on Jesus as the Messiah. Peter emphasizes that it is the name of Jesus that saves. This would be consistent with this specific speech and with one of the wider theological emphases in Acts.