In the three camera models (both Canon and the Nikon), can I have the same picture quality? I know it's a a very abstract and particular subject and it depends how best is the photographer but I mean, technically, any of those three can give me the same colour, lighting, sharpness quality?
In generally good lighting conditions, yes. In poor light, the better quality sensors will win because they produce less noise.
Which is usually better, make a pre processing configuration before take a photo or take a photo in a raw mode and make a pos processing to reach a specific result?
For quality of images and flexibility, shooting in RAW is better 100% of the time. The drawback of course is that it takes time to properly process images (some more than others).
In my case, I want to take all kind of photos but primarily I need a good camera for action photo and also which take good photos indoor. Considering these 3 options which one is more suitable for these needs?
I don't have experience with any of these, but the 7d is known to be a solid sports camera and will undoubtedly be better than the T3i. I cannot speak for the D7000.
About lens and filters, which one(s) you advise me to look for for canon or Nikon? The very necessary one(s)? I mean, if I could have just one or two which ones are the ones?
That depends on your budget. If I had a 7D and could only choose one lens, it would probably be the 24-105 f/4 L because it's sharp and covers a wide range of focal lengths. However, I don't own that lens because I am not restricted to just one lens. I have many lenses that do a better job than that one lens, but are not nearly as multi-purpose.
If you can help once more, you would made a happy guy, really!