For example Blog. Correct would be "das Blog" (because "das Web-Log" = "das Logbuch" or "das Protokoll"), but "der Blog" sounds nicer imho. Some people say "das Laptop" although this sounds off for most and "der Laptop" is correct.
For other words, the article can change over time. Correct is "das Virus", because it's a Latin word and the ending -us comes with "das". But most people say (and the media writes) "der Virus".
No. If something sounds right to a native speaker, it's correct.
As for the plurals, the -e suffix can often both be left out and replaced with an n, so you have two singular forms for some words.
But again, without the dialect it won’t work. As the GP said, you’ll still be understood, though. As with most languages, a lot of parts are superfluous and can be determined by context.
Another gem is that in my local dialect the word for foot (Fuß) has an extended meaning and denotes the body part of foot and leg. There basically is not a separate word for leg (well there is but it's standard German not dialect). The standard German word for leg is "bein". Now Bein has a common ancestor with a similar word in English "bone", and indeed the dialectal version of Bein in my dialect is the word for bone. (To me that indicates that the word has made a meaning change in standard German).
Now if I don't think hard (or if I am tired) I will call my leg "foot" in English, which confuses everyone.
Probably in German both meanings were used alongside for a while and then folks started to attach a "ge-" in front of one meaning to avoid confusion.
(And then there are Platt (= Low German) and Alemannisch/Schwyzerdütsch, both of which are distinct languages from High German.)
Nonsense. If a native speaker uses a form and thinks it's correct, it by definition is.
(A better example is “Mus”, which has multiple correct genders.)
German is a lot more prescriptive than English. This is only different for neologisms and anglicisms (“Newsletter”), where a generally accepted gender hasn’t been established through usage yet (Duden now lists “Newsletter” as masculine, but both “die Newsletter” and “das Newsletter” were common until recently).
Additionally, your explanation about the origin of the gender of “Butter” is entirely apocryphal: the original Greek/Latin gender has at best an indirect influence on the gender of the modern German word (and in fact both were neuter: βούτυρον vs butyrum).
An (Upper-)Bavarian would for example never say "die Butter". It is and will always be "der Butter". Same with "der Radio" in the South and "das Radio" for the rest of the country.
Another funny thing I stumble upon every time Oktoberfest starts: Oktoberfest in Munich is referred to as "die Wiesn" (the lawn/grassland). Bavarians don't know an 'e' in the end of a noun, they will therefore always replace it with a 'n'. In the rest of Germany, Wiesn doesn't exist. It's either 'Wiese'(sgl, a single grassland) or 'Wiesen' (pl, many grasslands). Since Wiesen sounds more similar to 'Wiesn' than 'Wiese', even newspapers regularly refer to the Oktoberfest as a multiple of 'Wiese' which - for us - sounds just wrong: "Heute sind wir auf den Wiesn gewesen".