How can infinitives, participles, gerunds.. act?

First a definition: There are three kinds of finite subordinate clause: relative, comparative and content. The latter lacks the special properties of the other two, and is regarded as the default kind. The term 'content clause' reflects its default status: it suggests that the clause is simply selected for its semantic content.

“That you can’t pick it up” is clearly not a relative or comparative clause, so it can only be a content clause. In the sentence “It’s [so heavy that you can’t pick it up]”, the content clause “that you can’t pick it up” is a complement because it has to be licensed (specifically permitted or required) by the “so” that modifies “heavy”. We know that because if we drop “so”, the bracketed AdjP becomes ungrammatical. The AdjP “so heavy that you can’t pick it up” is subjective complement of “was” – a complement because it is an obligatory item. The content clause is complement of “heavy”

We know it’s not an extraposition construction because “it” is referential – it refers to something mentioned earlier in the discourse, whereas extrapositional “it” is just a dummy subject.

Yes, “the fact that he never calls me” is a content clause functioning as complement of “fact”. “I hate that he never calls me” is OK in AmE but rarely heard in BrE. The content clause is complement of the verb “hate”. It’s important to remember that clauses can never be objects – only NPs can.