(What I find really funny is that some people show some sort of intuitive awareness of those regular sound correspondences, when dealing with closely related languages. I don't recall this among EN/DE speakers, but it's all the time among PT/ES ones: either joking "swap O with UE and you get Spanish" or "drop random consonants and you get Portuguese". Cue to "quiero una cueca cuela y un sorviete" pseudo-Spanish.)
Among the three you mentioned (language, dialect, creole), at least creole is well defined - it's the resulting evolution of a pidgin becoming a full-fledged language. At least in theory, because in practice we get partial creolisation and decreolisation of varieties.
A creole is by definition the descendant of a pidgin, a patchwork of words "glued" with some ad hoc grammar, that looks nothing like the grammar of the parent languages. A good example of that would be the Jamaican Patwa basilect:
* Dem a kuuk akara fi im (lit. "them are cook akara for him"; "they're cooking akara for him/her")
* Im a kuuk akara fi dem (lit. "him are cook akara for them"; "he/she's cooking akara for them")
Even if most words are clearly English (except akara - a fritter), the grammar looks nothing alike. It was rebuilt from the scratch. We can't really say the same about EME vs. LME, where there's a clear transition from one to another.
>from "it was never a 'true' creole because England still had an army on paper during the Norman Conquest" to "it stops being a creole when you have an empire and colonies are building their own creoles of your language" and all sorts of other ideas
The presence of an army or "metacreoles" is irrelevant. Kreyol for example would still be a creole, even if the Haitians built a thassalocracy.
What matters is the presence of a linguistic community, that kept speaking their language as they always did. Normans only replaced the local nobility, but the Germanic speakers were still there - speaking among themselves in their Germanic varieties, even if they had to butcher a "pig" or a "cow" because of some fancy noble wanting "porc" or "beof".
The evolution of languages is fascinating. Circling somewhat back to the topic above: the difference between "dialect" and "language" is a complex subject just as most "speciation" debates in other evolutionary fields have a lot of hidden complexity. "Language" versus "dialect" versus "creole" doesn't have a lot of simple answers though historically that joke that "a language is a dialect with an army" tracks more than it doesn't which is why it is a good joke.
[1] https://en.wikipedia.org/wiki/High_German_consonant_shift
[2] https://en.wikipedia.org/wiki/Great_Vowel_Shift
[3] https://en.wikipedia.org/wiki/Grimm%27s_law