I bought a new lens, and discovered two stains/spots which look like water spots on the rear side (side which is plugged to the body). These stains are from the inside. I have taken a couple of pictures but so far not discovered any problem. In some articles I read that a certain amount of dust comes ever with new lenses. Is it normal to have such spots even in a brand new lens (original Fuji)? Or shall I rather request an exchange of the lens?
The water spots could be from anything. Suggestion would be to return the lens and exchange for one which does not have any defects.
All of the "water spots" I've seen on the rear lens elements of my lenses were from my own mistakes, where a tiny droplet of water (breath, mist, cleaning solution, etc) landed on the element and was left there unnoticed. Some of them can be cleaned with a wipe, but others cannot. Depends on the coating formulation and on what liquid came in contact with the lens.
Since you just bought it, return it for another lens that doesn't have the defect. Ask to open the box and check when you buy the lens. Bring your camera, etc.
Before cleaning I would document the appearance of the lens when you unpacked it from the box. The sooner you do that the better so that the seller or warranty department doesn't think the spots could have been caused in your course of using the lens.
If the spots are on the outside surface of the rear lens element I would try cleaning them off with a pec-pad moistened with lens cleaner and followed by a dry pec-pad. If there doesn't appear to be any chemical residue on the pad from cleaning the lens it was probably just condensation.
Going from a cold to a warm/moist environment will cause condensation to form on lens elements. If the rear cap wasn't on tight and the lens was shipped via air cargo this could very well be the source of the water spots. When the water evaporates the dust that was in the water is left as residue. If it looks like there was condensed moisture at other places inside the lens I would strongly consider returning it. Use a flashlight to inspect the interior of the lens by shining at an angle through the front of the lens and looking through the back of the lens. Then do the reverse. (You will see dust. All lenses have dust in them.)
This issue is one reason it is important to insulate your gear when moving from a cooler to warmer environment. Always pack your gear before moving to the warm environment and then give it enough time to warm slowly before opening your bag. It is also important to pay attention to the temperature and dew point when shooting in cooler weather.
Many years ago I shot a lunar eclipse on a warm, moist night. By the time I went inside the dew was practically dripping off my camera and lens. Since it was cooler and dryer in my house with the A/C running I figured it would be okay to just wipe them down and leave them out to dry. The camera (a film EOS) was fine. The lens (a consumer grade Sigma 70-300), on the other hand would no longer auto focus. The moisture had apparently damaged the focus motor.