Does biorę have the same dual meaning as in English, like taking something like an object, and taking something like a more abstract thing?
short answer is "yes", but it depends. We have "brać" in figurative meaning but not all Polish meanings translate to English "take" and not all English translate to Polish. (Merriam Webster has 20 meanings for transitive take , and another 8 for transitive one. WSJP has 21 meanings for brać and 7 for brać się, not taking "wziąć" into consideration - some meanings of brać and wziąć do not match)
Yes, but I think that English "take" has much broader meaning than Polish "brać" or "wziąć" and it is used much more often in different contexts.
To me prysznic sounds very much as if she is saying prosznik, i listened a half dozen times and the word did not have the y sound to me.