Very noble and full of good intentions.
Best start with have you a professional solder station that has de-soldering capabilities ? If not best find one, fine tip temperature controlled to 400 deg.
Next best source ALL the components shown in the last two pictures you provided above. 6821's are becoming increasingly difficult to find. Work out how much it will cost you.
Then you need to remove all affected components, where the solder has turned green, white or dark grey or indeed any other colour other than nice shiny silver.
Then you need to scrub the tracks to remove the worst, then use a neturalising solution and repair any damaged tracks then start re-populating and soldering the replacement components.
I would continuity test each leg soldered to avoid problematic fault finding once the board has been repopulated.