Are rusting screws a sign of cheap/bad material? I noticed rusting screws at a ~ 1 year old bike and rusting screws at another bike after a few months, where the screws were part of a replacement (front gear ring package).

Both bikes were usually placed in rain protected places when possible.

Thus the question: Is this normal? Or do I have to change my bike dealer?

I mean, are not stainless screws standard? Or are they too expensive?
Stainless steel is rust-resistant not rust-proof, especially if the bike sees the outdoors a lot, it isn't uncommon for screws to get a fine sprinkling of brown spots. The good thing about screws is that they can be easily replaced.
If you were very enterprising you can probably replace your bolts with titanium ones. They don't rust in the same way as steel does at all. However, they are usually weaker than the equivalent steel bolts, so we would not recommend replacing bolts like the stem or seat clamp bolts without careful research on high-quality titanium bolts. If you do this, be sure to research titanium material grades; commercially pure titanium is likely too weak for structural bolts, whereas grade 5 (aka 6/4 titanium) is probably what you would want for these bolts. For reference, most titanium bicycle frames are made of grade 9, aka 3/2.5 titanium. The numbers for grade 5 and 9 reference the proportion of aluminum and vanadium in the alloy.
Painted components (like your bike frame) are naturally rust resistant because the paint prevents contact with oxygen, which means that the metal can't oxidise and also explains why its not a bad idea to touch up on large paint chips or scratches with touch up laquer.
ADDED a quick wikipedia glance explains that while stainless steel gets covered in rust, unlike regular steel the rust is passive meaning that it will just stay there (looking unsightly). With regular steel, rust has the nasty habit of eating away at the metal (it is an active oxidation site). The rust on stainless steel behaves like a coating that prevents further oxidation.
Additionally, see comments by @cmaster: not all steel bolts are stainless, particularly on lower-cost bicycles.