Is there a database/application that sorts characters based on pronunciation, radical, frequency; and disyllabic compound words by frequency?
I hope this pdf, Simplified Chinese Mapping Chart (1956), could help:
This is 简化字总表(Simplified characters full list), an official list that includes 1) simplified characters that may not be used as radicals; 2) simplified radicals and simplified characters that may be used as radicals; 3) frequently used characters.
Another even more comprehensive list with versions and alterations through years can be found on wikipedia 简化字总表 (Chineses only). I guess you would get what you were looking for by translating that page!