This is not a sentence, this is just the phrase en man, 'a man'. You don't say "he man" in English either, do you? If you were to say anything more about the man in this phrase, you should use the pronoun han (like: Han äter 'He eats'). But there are only two genders in Swedish, common gender and neuter, and all words that are referred to with the female and male pronouns hon/han are common gender, therefore it is en kvinna 'a woman' and en man 'en man' with the same article en, but if you speak more about them you use different pronouns, hon or han. Hope this helps?
I would assume that all language courses will feature pronounciation exercises when mature enough. But whenever that comes, I would take it with a grain of salt how good of an indicator it is to how good your pronounciation really is. From my experience with practicing French, I will sometimes pass a test even though I cancel the recording halfway through a sentence because I fumble with the words. Hopefully the accuracy will be better in the future, but until then just know that for the most part, the exercise is merely just for practice.
Not really lol, I'm intermediate in Japanese. But you're right Japanese doesn't always pronounce the full words for an example "desu" it means to be, they wouldn't pronounce the u at the end. Newspaper is actually pronounced as shinbun, but the n is a bit silent. The sh is more recognizable.
Spanish offerers a good example of what you are describing. The feminine 'agua', is preceded by the masculine article 'el', rather than the feminine article 'la'. All for the sake of flow. The plural: 'las aguas', functions quite well. 'La agua' however, would not be quite as elegant. The conjunction 'Y' (ee sound) is also replaced by 'e' (A sound ) when it would precede an 'i' (also an ee sound). The comon conjunction 'o' (hard O sound) is exchanged for an 'u' (oo sound) when it precedes another 'o', so that the matching sounds do not blend togather. Much as either 'a' or 'an' could be used in English.