Is PCI network card will perform better compare with motherboard integraded network card?

Answer 1

Both PCI and internal cards are capable of the same throughput. The speed is more often determined by the network signal then the card. Few networks are able to send through a signal that matches either cards maximum. So which you use is should not be an issue.

Answer 2

Probably not.

PCI cards will run at 100Mbit and so will built-in ones.

PCI cards will struggle to reach 1Gbit throughput... becasue the PCI bus can't cope with that throughput. Built in cards may have a higher speed bus than that.