[Quanttek]

I think that depends on what you mean: a general state of emergency or a specific situation where the police deem there to be an emergency (e.g. classic hidden bomb scenario)

Regarding (2), the Court found that a statutory obligation to decrypt E2E-encrypted data upon (judicial) request to be disproportionate, but it could still be imagined that – if more narrowly construed – a law could be considered to be proportionate. But the Court does seem quite unwilling to entertain the idea of backdoors for E2E encryption.

Regarding (1), the European Convention on Human Rights (ECHR) allows so-called derogations from certain rights in "time of war or other public emergency threatening the life of the nation" (Art 15 ECHR), insofar as they are necessary and the state of emergency has been properly declared. The right to privacy is such a right, so a State that faces an insurgency may declare a state of emergency and, as part of its emergency measures, could probably demand the decryption of E2E communications if it's necessary to fight the insurgency (e.g. it's a guerilla group using an E2E messenger) - but hard to judge in the abstract.