When you see it for the first time, yes, it is confusing.
"Venir" + de + another verb is used to say that you have just done something. This is called the "near past" or "recent past." The lesson you're doing covers this concept.
- Je viens de manger = I just ate.
- Il vient de le faire = He just did it.
It's nice to be able to ease beginning learners into the past tense.
Well, I can understand the male voice very well, it is way more crisp and clear. I think it is the microphone on which the lady has spoken the words.. They come out garbled, somehow. Mumbling Mabel strikes again, but like I said, I don't think it is her fault, I think it is an equipment problem.
Yes, you're right. I often have the same problem and have to check the pronunciation in my dictionary. Mostly when it is new word and my oldish ear cannnot catch it properly. I have the same problem in other languages, because the articulation is not the same as in my native language (Czech). Transcription in dictionary helps a lot to my ears what to hear in the speech.
The verb "venir" will always need "de" if you want to add another verb after it. So no, you cannot say "viens-tu parler".
As you continue with your French learning, you will realize that there are some verbs that use "de", and some that don't. Expose yourself to more French and you'll discover them.