With everything I've read, I'll try to respond to your questions more explicitly.
@Cfan said in Questions about CRA regulation(Cyber Resillience Act):
If I create an LGPL licensed app and sell it in EU(online sell), does CRA regulation apply to my situation too?
The only excemption from the CRA is non-commercial open source software. So, if you want to sell in the EU, your software will fall under the CRA. I am not sure what you mean with an "app under the LPGL". Is all your own code open source as well? Then you "only" need to follow articles 13 and 14. If your own source code is not open somebody has to follow more rules. If you are located inside the EU it'll be you yourself. If you are located outside the EU it will get more complicated. I am not sure what roles are distributed to "manufacturer", "importer", and "distributor". It might be that the app store might have to fulfill some of the duties instead of you yourself.
@Cfan said in Questions about CRA regulation(Cyber Resillience Act):
If my app does not use networking or internet, does it change something?
Yes. There is the category of "important products with digital elements". What makes a product "important" are things like internet connectivity. "Important products" have to fulfill additional obligations. Without any additional knowledge about your actual app I would guess that it is not an "important product". You'll find a list of important products in Annex III.