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Two questions:
1. How long does it take for on-page changes to effect KW rankings?
2. After the rankings update, should I immediately try to change low ranking pages, or is it better to wait some time between changes?
2. You can try. It may or may not have much of an effect. I'd try building another web page and linking it to the troubled one first. Wait a couple weeks. Then do on-page optimization, wait, then build another page with different links naturally flowing from unique content, wait, then optimzation ...
What does make sense is to make changes. Wait for a full crawl. Wait a week after for results. Wait a week more before making changes (to give yourself enough info as to what to change). Then proceed.
All this works at a snail's pace. It will not happen overnight either way.