Signals were not always analogue. Wire signals were sent with teletype using digital Baudot coding (a 5-bit character set), including in encrypted form using for instance the German T52 Geheimschreiber. Although the radio transmissions used were analogue, the Enigma cipher itself is digital; one discrete letter becomes another; it's not one continuously-variable signal being transformed into another. In present day terms Enigma the T52 and similar are what's known as stream ciphers (as opposed to AES which is a block cipher)

The question is odd; There's no known attack on AES in the present day, and no reason to assume WWII cryptographers know anything today's don't. (rather the opposite; I think it's safe to say that in terms of published volume; more cryptography research is done in a single year these days than had been done in human history prior to WWII)

As for decrypting it with a known key (and knowing the method), that would certainly be doable. You could even do it with a paper and pencil if you liked, tedious as it'd be. There are no fundamental mathematical/logical operations involved that weren't known at the time. Ciphers like AES are not really that complicated; it's a design goal that they should be simple and fast to implement in computer hardware. Simplicity is also important to aid the cryptanalysis. In short, the more complicated a cipher is, the bigger the risk there's some hidden vulnerability, and a common maxim of modern cryptography (also voiced by some WWII cryptographers like Arne Beurling) is that one should not rely on obscurity and complexity for security.