If you listen carefully, in the first audio sample the /ø/ is sounded, albeit faintly. It makes sense, because the man uses a [z] liaison between veux and attraper, and as @None pointed out, you cannot chain two elisions or it would result in three consonants in a row: [ʒvz]. Some vowel has to be inserted somewhere.
What you might have in mind is that two consecutive vowels sometimes tend to merge. J'veux avoir and j'vais avoir mightcan indeed sound extremely close.
In the second extract, not only je vais t'en but really all the words are mashed together. It's very unusual, not recommended for clear communication and probably dictated by rythm and verse length in the song. It also sounds like he says rouge, not rose.