Usage of "there is/there are” anticipatory clauses

As the Covid-19 pandemic became resurgent last December just when we thought it was finally tapering off for good, there's now an even more pronounced but understandable paucity of new grammar questions getting asked in the Forum. I am therefore taking this lull as an opportunity to revisit a very contentious aspect of English grammar that has perplexed not just a few Forum members over the years. It's the dilemma over subject-verb agreement in "there is/there are" clauses that Forum member Sky presented in the Forum almost a decade ago.

Sky's question: "Are native speakers of English correct when they say: (1) 'There's only five classes on the second floor.' (2) 'There's many students not attending their classes.' (3) 'There's only two classes I got today'?"