The software being free and open source has no impact on whether it infringes any patents or violates any copyrights.
Copyrights attach to fixed representations of creative work in a tangible medium (e.g., the actual code and graphical elements of the software in question). As long as you aren't copying the copyrighted work of someone else, you should be in the clear. So, if you write your own code from scratch, or rely on code that you're allowed to use (e.g., "free" software with a permissive license that allows it to be used freely), you should be fine. On the other hand, if you copy a chunk of code that you aren't allowed to use, and then change the variable names so that it's superficially different, you're likely violating someone's copyright.
Patents are a much more difficult question. To determine whether you would infringe any patents, you would have to read the independent claims of every patent that might be related. If you perform all the steps of any one of those claims, then you are infringing that claim (and therefore, the patent in which it is found).
Unfortunately, this is much easier said than done. First, it may be difficult to search for all the potentially relevant patents, and once you've found them, there may be far too many to read. Second, claims are written in a type of language that is specific to patents, and someone without experience in patent law may not understand them correctly. Finally, the terms in the claims may not take on their plain English meaning, but rather may have been defined by the language in the rest of that patent, so it's possible that you might incorrectly think you were in the clear based on a misunderstanding arising from that.
All that said, it may be best to go ahead with implementing an idea and then waiting to see what happens. Chances are that the implementation will arguably infringe some patent in some way, no matter what's done. But chances are also high that there will never be any worrisome enforcement action taken against it by a patent owner, simply due to the difficulty and expense associated with enforcing patent rights.