"Het hert heeft honger en is zwak."
Translation:The deer is hungry and weak.
I understand it can be difficult, and the voice is not perfect. However with my native Dutch ears I can understand it perfectly. So all I can advise you to do is, keep on trying, use the slow voice (turtle icon) if you need it. And try to just keep on listening and speaking yourself (for instance you can repeat all sentences out loud), you'll get more used to it over time. Also you don't have to limit yourself to Duolingo, you can e.g. listen to Dutch music.
Right now a bunch of DJs and Within Temptation are best known internationally indeed. But there is a lot more, most of it only well known in the Netherlands and Belgium.
There have been quite a few threads on Dutch music, so you can find a lot of tips here. A good tip for Dutch learners is Eefje de Visser.
In the word "zwak," my native English brain is perceiving more of an English "w" sound than a "v" sound here. Until now I've been accustomed to pronouncing the Dutch "w" as closer to the English "v."
Is there a difference here or are my ears playing tricks on me? Also, is there a good general rule to keep in mind?
The Dutch 'w' does not sound like the English 'w'. But imo, it doesn't sound like the English 'v' either.
Look at this:
Looking at IPA, the Dutch 'w' does not sound like the English 'w'.
According to wikipedia, /ʋ/ is pronounced like an English w, with the teeth and lips held in the position used to articulate the letter V.
For this sentence, Ruben pronounces 'zwak' just fine, like a native. :)