I had links at my site in 9 pages uncategorized. I have read that having categories is more effective so I would like to do so. Anyone dealt with such procedure? How to make it more effectively without loosing PR of the pages? when it is better to do? and how to deal with link partners?
Appreciate your help a lot!

This won't help you at all. Keeping the external links in your site in an organized bundle does not affect your rankings. It would only affect the rankings of the sites you link to. Even then, reciprocal links are useless for SEO anyway. I wouldn't worry about this or waste your time working on it.

oh dear... why is all that fuss about?
"It would only affect the rankings of the sites you link to" So you mean that it should be not reciprocal links but only my links somewhere to make it work?
What is the solvation? directories and general publicity?

Organizing the links to other sites will only affect the links to the other sites. It won't affect the rankings of your pages. Unless you care how your link partners rank I wouldn't consider this worth doing.

Reciprocal links don't help with SEO. Google has devalued them as they should. One way incoming links are what you need.