Both can be used in both contexts. Effectively, when given a negative connotation, it is similar to the word 'Stunned' as in "I will be amazed when he finally gets a job" or "I'm astonished by your lack of commitment". Realistically, it depends on what follows these phrases in the sentence as to what the connotation will become.
Compared to the first two expressions, "be fascinated, captivated and mesmerised" are more about curiosity. These kinds of phrases usually are seen as positive and are strange if followed by a negative sentence, for e.g. "I am captivated by his ugly face" Naturally, a sentence structure like this is not used by native speakers and instead positive connotations are adopted. Hope this helps!