Right now I'm developing mostly in C/C++, but I wrote some small utilities in Python to automatize some tasks and I really love it as language (especially the productivity). 
Except for the performances (a problem that could be sometimes solved thanks to the ease of interfacing Python with C modules), do you think it is proper for production use in the development of stand-alone complex applications (think for example to a word processor or a graphic tool)?
What IDE would you suggest? The IDLE provided with Python is not enough even for small projects in my opinion.
You'll find mostly two answers to that – the religous one (Yes! Of course! It's the best language ever!) and the other religious one (you gotta be kidding me! Python? No... it's not mature enough). I will maybe skip the last religion (Python?! Use Ruby!). The truth, as always, is far from obvious. 
Pros: it's easy, readable, batteries included, has lots of good libraries for pretty much everything. It's expressive and dynamic typing makes it more concise in many cases.
Cons: as a dynamic language, has way worse IDE support (proper syntax completion requires static typing, whether explicit in Java or inferred in SML), its object system is far from perfect (interfaces, anyone?) and it is easy to end up with messy code that has methods returning either int or boolean or object or some sort under unknown circumstances.
My take – I love Python for scripting, automation, tiny webapps and other simple well defined tasks. In my opinion it is by far the best dynamic language on the planet. That said, I would never use it any dynamically typed language to develop an application of substantial size.
Say – it would be fine to use it for Stack Overflow, which has three developers and I guess no more than 30k lines of code. For bigger things – first your development would be super fast, and then once team and codebase grow things are slowing down more than they would with Java or C#. You need to offset lack of compilation time checks by writing more unittests, refactorings get harder cause you never know what your refacoring broke until you run all tests or even the whole big app, etc.
Now – decide on how big your team is going to be and how big the app is supposed to be once it is done. If you have 5 or less people and the target size is roughly Stack Overflow, go ahead, write in Python. You will finish in no time and be happy with good codebase. But if you want to write second Google or Yahoo, you will be much better with C# or Java.
Side-note on C/C++ you have mentioned: if you are not writing performance critical software (say massive parallel raytracer that will run for three months rendering a film) or a very mission critical system (say Mars lander that will fly three years straight and has only one chance to land right or you lose $400mln) do not use it. For web apps, most desktop apps, most apps in general it is not a good choice. You will die debugging pointers and memory allocation in complex business logic.
Is Python good for big software projects (not web based)?