"The man has a spider."
Translation:Der Mann hat eine Spinne.
Der is used for masculine nouns, but also specific masculine nouns. Der is used when using accusative case, which is when you are talking about what a man is doing, for example. Die is not used because it is only used when there is Frau, or when there is multiple things being talked about, like die Frauen, or die Frau.
einen would be used before a masculine noun -- for example, Der Mann hat einen Hund "the man has a dog", since Hund is grammatically masculine.
But Spinne is feminine, so the correct form is eine Spinne here.
And a neuter noun, e.g. Pferd, would have been ein Pferd.
In general, if a spelling mistake results in another valid word, Duo marks it as an error as it can't tell the difference between an honest mistake and deliberately typing the wrong word (perhaps because you learned it wrongly).
Both man and Mann are valid German words, so if you write der man (or even der Man -- Duo generally ignores capitalisation), it assumes you meant to write that, and marks it wrong.
If you had written der Nann, you would probably have got a typo warning, since Nann is not a word and so it's probably a typo or finger-slip.
Apart from sounding silly, how would using the incorrect "the" words effect communication?
It may just sound wrong or it may actually impede communication.
die Mann just sounds wrong, but if you said die Mädchen instead of das Mädchen, you've turned it from "the girl" (just one) into "the girls" (many of them), and if you said die Leiter instead of der Leiter, you've changed the meaning from "the leader" to "the ladder":
Most of the time, using the wrong article will just sound odd and wrong and mark you as a foreigner/learner, but sometimes it can actually cause confusion.
in Animal eine is a and ein is An?
The use of ein, eine, einen depends on the grammatical gender and case of the following German word.
The use of "a, an" in English depends on the sound of the following English word.
The two have no relationship to each other.
"a" is sometimes ein, sometimes eine, sometimes einen.
"an" is sometimes ein, sometimes eine, sometimes einen.
ein is sometimes "a", sometimes "an".
And so on.
How do you know if a noun is masculine or feminie
You have to look it up in a dictionary and memorise the answer.
Since you usually can't guess the grammatical gender of a noun in German, any good dictionary will give the gender of each noun, often with an abbreviation such as m, f, n for "masculine, feminine, neuter", sometimes with r, e, s as in der, die, das.
There can even be two nouns that are spelled the same but have different genders.... (For example, der Leiter = the leader, die Leiter = the ladder.)