No, it's not you, you will not hear the "ent" at the end of third-person plural verbs. But you will hear the "V" in "ils écrivent" which is not pronounced in the third-person singular form (il/elle écrit). Listen carefully for the "V" and voilà, problem solved. You will also hear the "S" of "ils" or "elles" when it is followed by a vowel because the two words are pronounced with a liaison (run together). That is another clue that will help you. These same clues may be found in many French verbs if you listen carefully; unfortunately not all of them!
Il écrive and Ils écrivent are pronounced basically identically. You wouldn't always run the s into the next word (or you would end up with the odd 'Il s'écrive' - he writes himself) so it will be hard to tell the difference.
The -ent ending isn't pronounced, and this is correct as mentioned by csueiras.
If you listen to Duo at fast speed you can hear both the s at the end of ils and the v in the middle of écrivent where the spoken part of the word ends. Either one of these is a tipoff that plural is required. You hear the v because it is there. It is there because it is followed by ent.
Google Translate pronounces it the same way. Forvo not only pronounces the s it is so clear you hardly hear the rest of the word. Both of them have a subtle v in saying écrivent.
Most English speakers do not go out of their way to make sure should have does not end up sounding like should of. They also sometimes say going as if it was goin. They leave it up to the listener to either hear the subtle sounds or deduce the correct form.
The same is true for French. Most French speakers in ordinary conversation expect you to figure out what is being said. They don't spend a lot of energy and time emphasizing clarity just to make it easier for the listener.
Duolingo is not he proper approach to learn to understand spoken French. Nor should it be. Other platforms are available that do that.
It consists of translation exercises most of which are based on reading. Duo makes no attempt to assist students by ensuring quality of sound. It does not introduce vowel paring to train the ear. It doesn't even mention the elements of the mechanics of producing French language sounds.
The few Duo examples that do involve translating oral presentations should be seen as an indication of what you don't know. For all their lack of clarity they are much easier to deal with than regular conversation among French people.
Even though the French verbs do not have a continuous form, context would express whether the subject is "in the process of doing something" (basic meaning of a continuous present) or "does something as a habit".
If we really want to convey that an event is happening right now, we use the periphrase: "être en train de":
- they are writing (right now) = ils sont en train d'écrire.
You need context to understand some sentences in French (as in English but less so). Luckily, people hardly ever walk up to you and say something at random that can only be understood with context.
Unfortunately, translations exercises are full of comments that are hard to really understand without context.