If my phone carrier is Verizon can I still get a replacement phone from apple store?

Warranty replacements can be handled either by Verizon or by Apple. The big difference is that, if you go into an Apple Store, they will generally hand you a replacement on the spot. Verizon will have to order it for you. Depending on whether you've paid for additional warranty coverage, the phone might come overnight or it might come in 5 business days.

if your device is under hardware warranty and the issue is hardware, you can exchange it at an apple store

if it's accidental damage (dropping/screen crack, etc), i believe the price is $149 for a new phone, also from the apple store

No.

Apple handles all iPhone exchanges under Apple's warranty in the US regardless the carrier.

Accidental damage not covered under the warranty.

Apple's out of warranty or not covered under the warranty "repair" price which pays for an exchange at a discounted price off the full retail sales price can be done at an Apple store as well regardless if the iPhone is activated with AT&T, Sprint, Verizon, or was purchased as officially unlocked.

Apple handles warranty replacement for all phones, regardless of the carrier.