Depending on how you define "dialect" or "language", they may or may not be.
To quote the obligatory quip: "A language is a dialect with an army and navy".
I recently watched the Swedish production "Blue Eyes" (with English subtitles), and was amused at the amount of speech which struck me as being 'English with an odd regional dialect'. Usually these were simple 'core language' statements and / or imperatives.
I guess that is more the lasting Viking and Dane Law impact upon the English, than English feeding in modern Swedish.
It might be the result of common Germanic grounds, not necessarily lateral influence. I got the same when learning German - sentences like "das Haus ist rot" or "ich trinke Wein" are surprisingly easy to catch up from English. And after some time you start noticing patterns, that help you further.
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
(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".
There's definitely some similarity between the two Germanic languages, but the North and West Germanic languages had started to diverge by the point of Danelaw, though the Battle of Maldon does record the languages as being mutually comprehensible at that point.
And more importantly: I don't think there were a lot of sound changes triggered by Norse influence, and those are the most relevant factor behind mutual intelligibility. Some odd non-core vocab here and there is easy to skip, and still get the "rough" meaning of a sentence, and speakerers cannen sentencen still understanden, eben mit somes oddes endinges.
It's up to the linguistic community to decide that, if their variety should be considered a "dialect" of something else or a "language" on its own. Linguists already gave up that question, it's more useful to talk about varieties anyway.
And it's the same deal with Galician versus Portuguese, with a difference - "Scots is a dialect of English" threatens Scots, but "Portuguese is a dialect of Galician" doesn't threaten Portuguese (it threatens Galician instead).