Discount Points and Penalties

What do you think this brief paragraph is saying?

“(1) Discount points should lower the interest rate paid on the loan but may not lower the overall cost of the loan. (2) If you refinance or pay off your loan quickly, you will lose the benefits of any lower interest rate provided by the discount points. (3)Furthermore, if you financed the discount points, this will increase the amount of money that you must repay to the lender and you will have to pay interest on the discount points as part of the amount you have borrowed.” [Note: The numbering is mine - added for clarity of discussion in this thread.]

Mu questions:
RE: Statement (1): If discount points (DP) lower the interest, then how can they NOT lower the overall cost of the loan?

RE: Statement (2): “…Lose the benefits of any lower interest rate provided”? Does that mean, when paying off in full early, I now owe them the whole non-discounted interest rate???

RE: Statement (3): I plan on financing the DP amounting to say $250.00, but if I pay off early, I’d now owe $250.00 + X …before interest? AND! Am I to understand I’d owe more interest than the interest I am paying to pay-off the loan? And, that would be at the non-discounted interest rate? …Or, higher?

How would you interpret all this? Would you assume “paying off quickly” would include receiving such penalties for making the regular payment PLUS partial payments - to pay off early?

Thanks!