Learn English – Can “On a second look …” be used in a sentence

Yes, the first sentence is as correct as the second. In fact, although such inversions are sometimes awkward, I can't think of a case in which a comparable inversion would be incorrect. In this case, I'd prefer the first version, because it moves the verb forward, and shifts a very long noun phrase to the end.

It's not at all uncommon; here's a line from a translation of Pippi Longstocking (quoted here) that does it:

Way out at the end of a tiny little town was an old overgrown garden, and in the garden was an old house, and in the house lived Pippi Longstocking.

No, this does not work. "All of which will dampen the customer service experience JetBlue values so highly" is a relative clause, and as such, it is dependent. Only an independent clause can be used in a sentence on its own.