Not sure

That's an engineered wood called longstrip. Yours is a 3-strip where three rows of smaller boards are laminated to each piece. It was one of the first floors that came prefinished with a square edge. It started out being made in Scandinavian countries, with a hardwood surface, softwood lumber core and backing. Popular brands are/were Kahrs, Tarkett and Boen. They almost always have a urethane/lacquer type finish so it's odd that it would stain easily. They are susceptible to moisture intrusion and if you have termites, there may be a relationship between them and the moisture issue. The veneer on your floor appears to be White Oak.

So does that mean it's neither laminate nor hardwood? Maybe it stains so easily because it is dark, I don't know but I mop everyday with a clean mop it is driving me insane and even then I can't get rid of white marks left behind from my parrot pooping around. I wipe the poops immediately and I use a vinegar solution with a microfiber cloth but there is always a white stain.

Is this type of flooring easy and cheap to replace like laminate?

According to Timothy Winzell that's an engineered hardwood.

Hardwood is a term generally used to refer to deciduous trees and their product. Many people mistakenly use the term to refer to solid wood. Softwood is a term generally used to refer to evergreen trees and their product. Hardwoods grow more slowly, are harder/denser and make a more suitable wearable surface.

Laminate generally means a fake wood type product and is often called plastic laminate. After cheap plastic laminates came out, the wood industry started using the term "engineered flooring" to refer to laminated wood flooring. You don't have laminate. You have engineered wood flooring with a hardwood surface (White Oak) and layers of softwood in the construction. This can be done for reasons of stability, environmental efficiency and in some cases, tax advantages.

Someone may have applied an acrylic wax/polish over your floor. Try using a little ammoniated glass cleaner and see if it removes the white spots because a urethane finish shouldn't be affected by the bird poop.

Your loose pieces can be reglued with a product like Titebond or Elmers Carpenters wood glue.

I haven't priced a longstrip replacement in a very long time but I suspect that it would run around $12 per square foot plus removal, trim and painting. Quite often they are laid floating over a foam. They generally have a thick enough top veneer to allow for a resanding or two.