Hi there,
I think, first off, the example sentence you gave is a question of PRONOUNS, not of SUBJECT-VERB agreement.
"A team of researchers conducted the first study of how baby and adult brains interacted during natural play, and they find measurable connections in their neural activity."
A 'team of researchers' would, indeed, take a singular verb. I suspect you're wondering about the 'they find measurable success,' because 'they' is a plural pronoun and 'find' is a plural verb.
But 'they' isn't referencing the 'team.' 'They' is referencing the researchers... and that's allowed. There aren't many rules for which noun a pronoun can replace.
"A pack of wolves stalks a deer through the forest, and they will eat it heartily when they catch it."
[Sorry to the deer and to any vegans, that was the first sentence that came to mind].
So the subject in the first clause is the PACK of wolves, but the subject in the second clause (NOTICE THE CONJUNCTION 'AND') is 'they' (the wolves themselves).
In your sentence 'team' is the first subject, and 'they' (the researchers) is the second.
"one of my students" would take the singular: "One of my students is getting a full scholarship."
Here's the trickiest one: "A number of my students." Number is singular, right? And 'students' is in a preposition. So this is like 'team of researchers,' it should be singular, right?
Well... it's not. "A number of my students" means "more than one of my students" so it would actually take the plural. "A team of researchers" means one team [of multiple researchers], so it takes the singular.