The reason is was marked wrong was the sentence stated "die Jacke". Your entry would translate to "Ich trage EINE Jacke." "I wear A jacket."
Umlauts only show on 2nd and 3rd person singular. Ich trage, du trägst, er trägt, wir tragen, ihr tragt, sie tragen.
No, not at all.
Just as English speakers don't get mixed up when Er sagt, dass es regnet and Er sagt, dass es regne both get translated into "He says that it is raining" -- how can you tell whether you agree with what he says or whether you're explicitly marking the words as being a quote and not necessarily something you can confirm?
Different languages grammaticalise different things.
Germans don't think they're missing anything just because they don't have a distinction like that between English present simple and present continuous -- just as I daresay essentially all English speakers have essentially never felt the lack of a vigorous subjunctive mood to be a problem at all.