Honestly I don't think 'threatened by tuberculosis' does have to be a set-phrase. Both threatened with tuberculosis / threatened by tuberculosis - sound okay. Likewise threatened with violence / threatened by violence - etc. I think both are okay. Maybe there is some tiny difference in nuance but most native speakers wouldn't notice it. As for 'pale with anger' - I think this is more of a set-phrase and just needs to be accepted for what it is. We use this structure when describing how emotions affect the body: pale with fear red with rage seething with anger sweating with indignation I think you could insert something like: pale with [the feeling of] anger. I think this is probably what is being implied.

Whenever you use a past participle (such as "threatened" or "surprised") as an adjective, you create an unspoken subject. For example, if you say "There is a buried treasure under the tree" then the person who buried the treasure becomes an unspoken subject. "By" reveals that unspoken subject: "There is a treasure buried by Bill under the tree." You can also use "with". However, the meaning might change radically: "There is a treasure buried with Bill under the tree" has two possible meanings. On the one hand, it could mean that Bill was present when the treasure was buried. Unfortunately, it could also mean that Bill and the treasure are buried together under the tree. "Threatened with tuberculosis" and "surprised with this" are valid expressions. The use of "with" does not make explicit that "tuberculosis" and "this" are the causes of the threat and the surprise, although this might be inferred. Sometimes, however, that inference might be false: "The man came home to an incredible meal his wife had prepared for him. Never had he eaten such an amazing meal. He was also tired after a difficult day at work. He was surprised with time to rest at last."