Is it normal that the tyre fits effortless the rim?
Not all tires are hard to put on (depends on type) and rims also have a variation in size (both between different types of rims and sample to sample variation within one model). In fact, I'd say many tires for urban and mountain bikes can be mounted without tools if you know how to. There are obviously counterexamples that are notorious for being tight.

Unless you can get the tire off easily and without tools too, you should be fine.