Can it happen that we don't own the IP rights to our code?

It depends on whether you have executed the proper agreements with your developers, which also depends on whether the developers are employees (subject to an employment agreement that has compulsory assignment provisions) or contractors. These issues can have implications for both patent and copyright analyses. The patent issues are quite separate in their analysis from the copyright issues, as ownership (authorship) and inventorship are two different discussions.

Depends on what IP rights you sought, copyright is a pretty standard "work-for-hire" arrangement but what about the preliminary UX/UI skeleton drawings (potential tradedress), or the beta-customers (commercial trade-secret). Ownership can be nebulous in that some software requires underlying libraries which may have licensing / distribution constraints. In Europe moral rights also come into play but that is rarely invoked. In short, the 3 you need to focus on are copyright, trade secrets and trademarks/tradedress (UX/UI) to make sure the assignments are evidenced in writing (contract) and formal registrations are under your company name.

Your code and UIs may be subject to open source licenses if you derived it from OSS or packaged it with OSS.
Your code may also infringe existing patents, and you may need to then license those patents in order to make, sell, or use your code (plus a few more limitations)