Presently, my 2" PCV pipe from my washing machine ends in the attic. I would like to extend the PCV to the roof, and want to be able to purchase a roof vent that would prevent bires and rodents from entering.

You are right in your thinking that the vent should terminate on the outside of the roof, not inside, its code. Most vents terminate with just a staright section of PVC expose to air with no cap or screen. Screens get added when folks have trees dropping junk or other debris, your call but not necessary

The white pvc pipe in the attic is a vent pipe. A vent system is a code requirement for all drains. They most often serve more than one drop (drain.) It should go through roof using a plummer's pipe vent often called a boot. They are sold at every home improvement store in the roofing materials section. They should be installed on the roof slope with upper shingles overlaping the upper edge of the flat part of the boot. Sending it through the roof will not improve the drainage but will get the potential odors and gases that could be in the drain system. Rarely are they topped with any kind of cover to prevent entry. However, simple screen wire would work if you expect to have problems and not interfere with the air passage.