JetBlue used to be more point-to-point, but they now sell just as many tickets to connecting passengers.

They are somewhere in between. They will launch service to where they think they can make money, even if it's not inside their network at all, such as SEA-ANC and PDX-ANC to compete with Alaska.

Allegiant is entire point-to-point. But even Southwest and Spirit sell connecting tickets now as well.

Also, Ryanair just launched a feeder relationship with Air Europa.

For checked bags, yes they will.