Normally, the -ness and -ty suffixes seem to be translated to -heit or -keit. But for busy-ness ("Beschäftigkeit"?), angriness ("Wutigkeit"?) and further "-ness" words it apparently isn't used. In the case of -ism to -ismus there seems to be no bigger problems.
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I don't think such simple one-on-one rules exist. In addition to -heit and -keit, there are also -nis, -schaft, -tum and -ung as typical noun endings, creating nouns from both adjectives and verbs. Your examples are very different in German:
Business can be translated as Unternehmen, Angelegenheit, Sache or Pflicht (or many other words). Depending on the chosen translation of the adjective "busy", you may not find a real noun from it (beschäftigt => Beschäftigung, but the latter is not a translation for business). Or take fleißig => Fleiß, eifrig => Eifer and so on. Not easy.
Angriness is Wut - here the German adjective is created the other way round (Wut => wüten (verb) / wütend (adj.)).
Words ending with "ism" in English and "ismus" in German are typically derived from the same Latin base. But a lot of words in German, of course, have Germanic roots.