How to balance previous works and current idea in a research plan?
This is a lot of questions wrapped into one, but let's give this a try. LOL!

First, is this part of an application for a faculty position? If so, 5 pages is very long. The faculty search committee will have statements from many candidates and cumbersome application materials may not get full attention (I've been on a number of search committees and have been chair of search committees). So, try to get it down to 2 pages and stick to the basics. If you are using this statement for something else and have a 5 page limit, disregard this suggestion. 

My advice is to try and find a unifying theme that all of your three sub-themes fit under. Then, introduce the larger theme and go into sub-themes A, B, C. Rather than dedicate a specific percentage of space for each (you indicate 50%, 50%), I would spend more time describing how your previous work resulted in specific skills, accomplishments, accolades, awards, grants (etc.) and then discuss briefly what your future plans are. I say this because your future research plans may change based on new opportunities and challenges. 

The purpose of most research statements is to (a) describe your area and its importance, (b) demonstrate that you can be successful at research, and (c) can articulate a reasonable plan for securing funding and independently conducting studies in the future. Also, writing too much detail about your future research plans may work against you if a reviewer disagrees with some aspects of your plan. Consider that as well. 

I would include citations, where appropriate, in the research statement, but only in-text. I would assume that the reviewers can cross-reference your CV, if it is also given to them. 

Good luck!