Is it perfectly acceptable to take off a fitting and solder a coupling to it, as opposed to going back and soldering to virgin pipe?
Nothing wrong, except that it is more difficult to re-use a fitting or resolder to a length of pipe.
The solder residue from the previous time might be too bulky to fit the parts together.
For one reason or another, the joint made with re-used parts often develops oxidation inside during reheating and the solder doesn't seal the joint properly and it leaks.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.