You slightly misspelled it, but רואה has two pronunciations. If a male is speaking it is pronounced ro'eh. If a female is speaking it is pronounced ro'ah. Both male and female forms for this verb are spelled exactly the same רואה. This verb type is very common in hebrew and the reason the form is slightly different from other verbs like אוכל / אוכלת, where you add ת to make the feminine, has to do with the root of the word. You will learn that later.
Just to clarify:
What determines the gender of the verb is not the gender of the person who is speaking the sentence, it's the gender of the person who is the subject of the verb.
So, in the sentence on this page, although the recording that played for me is spoken by a man, the verb is feminine singular because the subject is "הילדה", "the girl".
If you pay close attention while listening to any language you already know, you'll notice words blending together like that, too. It's how we end up with weird misunderstandings of song lyrics, for example. "Lady Mondegreen" is a famously misheard lyric (actually "laid him on the green"). With practice, you'll start to hear where words begin and end better. Be patient with yourself!
The pronunciation is good, in my opinion. It's not faster than how you'd normally say it, maybe even a bit slower (the speaker pauses a little bit after רואה). Don't be discouraged though, the listening exercises are difficult at first, and the missing "slow" button makes it even harder in the Hebrew course.
It's not silent, it sounds somewhat like French 'r'. Here is the article about the consonant in Wikipedia, there's an audio on the right template.
There is no slow button because these are human recordings (not TTS) and Duolingo does not support slowing down the speech in such courses.