why do we say Dutch in English if it's Nederlands in The Netherlands? It sounds like we confused German ("Deutsch") and Dutch as the same word.
Short answer: it's not wrong, but it's linked to some complicated history and no clear distinction between the languages Dutch and German and their predecessors.
I'm no expert, but what I could quickly find about it:
It goes back to the late Middle ages when a early forms of Dutch and German were spoken: dietsc and duutsc refer to variants of the Germanic languages. These terms were mostly used to distinguish both Dutch and German from Roman languages and can apply to either Dutch or German. The distinction between Dutch and (low-)German (Nederlands en (Neder-)Duits) was not that clear.
The English word Dutch is derived from duutsc or duutsch
Also in Dutch the word Duits (current meaning: German) was used to refer to Dutch (Nederlands) up to the 17th century. This can for instance be seen in the Dutch national anthem (sung from the perspective of Willem van Oranje), the second line is:
ben ik, van Duitsen bloed (am I, of Dutch/German blood)
Also see this explanation in Dutch: https://nl.wikipedia.org/wiki/Nederlands_(naamsgeschiedenis)#.C3.9Eeudisk_in_de_volkstaal
All I'd really add to that would be that as I understand it the term(s) which ultimately became Dutch in English and Deutsch in German meant something like "vernacular" and/or "of our people". The Dutch used the words mentioned to designate themselves and their language as the Germans do today. We (English speakers) adopted their term as our term for them. However, we already had a term for the region that is now Germany (what was the the Holy Roman Empire), which was derived from the Latin Germania, so we used that instead to refer to Germany, German and Germans.
Technically, native speakers call 'Dutch' 'Nederlands' which is also on DuoLingo I believe...
Does 'Nederlands' specifically mean the Dutch (as opposed to Belgian) dialect of Dutch? Would someone in Belgium, speaking Flemish, say 'Ik spreek Nederlands' (differences in the grammar of the sentence aside)?
As my Belgian teacher says. 'Nederlads' is the official language both in The Netherlands and in Belgium (Flemish region and Brussels) . Flemish is a dialect.
I'm no expert, but they would say, "Ik spreek vlaams." "Vlaams" is Flemish for Flemish.
It's as OscarHermosilla mentioned, there's only one language spoken in The Netherlands, Belgium and Suriname. The only odd thing is that there is a term for the group of dialects spoken in Flanders, but there is no term for the group of dialects spoken in the Netherlands.
It's fine to say Ik ben een Vlaming en ik spreek Vlaams just as it's fine to say Ik ben een Brabander en ik spreek Brabants.
"there is no term for the group of dialects spoken in the Netherlands" Sure there is, at least in Belgium and most of the rest of the world, it's called 'Hollands'. Of course this is a historical inaccuracy caused by tradesmen from Holland spreading the concept of 'Holland' worldwide, but it is what it is.
what's the difference between, Nederland, Nederlands, Nederlander, Nederlanders
Nederland is the country, Nederlands is the language, Nederlander is a citizen of NL and Nederlanders is a plural form of Nederlander.
Should I completely ignore 'r' in pronouncing "Nederlands"? She's saying it like " needle lands".
Nope. The r is indeed pronounced softly (even very softly by some people), but it definitely is pronounced.
I'm the same level as you, but I would guess it would be "Ik spreek geen Nederlands." The sentence in German would be "Ich spreche kein Niederländisch" or more colloquially "Ich kann kein Niederländisch."
Does the "i" in "ik" have to be capitalized like the English "I" or does it have to not be capitalized? Or could it be written either way?
Nope not like in English, it's just a normal word, so it is only capitalised here because it's the first word of the sentence.
I got it wrong for typing "Ik spreek Nederlandse". Is there a reason for this?
Because Nederlandse means Dutchwoman or is the adjective for Dutch.
The language is "Nederlands".
Not like in German; scroll up and read all of the moderator Susande's responses. She has already answered this and here is another place to listen to different people saying this very sentence: https://forvo.com/word/ik_spreek_geen_nederlands/#nl
I am not an English native speaker so I have this question: Do we also capitalize languages’ names in Dutch?
Yes, language names and nationalities are considered proper names/nouns ('eigennamen'), so they're capitalised in Dutch.
For the word spreken you could think of it as ik and spreek both ending in a k. However, it may be more useful to learn the general rules for Dutch verbs. Generally the 1st person singular form of a verb (that’s the ik form) doesn’t have any ending added to it (so spreek); all other singular forms add -t (so jij spreekt). Plurals add -(e)n and if there is a doubled letter in the middle it becomes a single one (so wij spreken). It isn’t always that simple but usually follows that structure. Important exceptions include hebben, which changes to jij hebt but hij/zij/het heeft, and zijn, which changes to ik ben, jij bent and hij/zij/het is.