If too many people are occupying a small space, then one of you may be "squeezed out" i.e. expelled through physical pressure. The exercise here uses the same verb - squeeze out - in the context of teaching the "schwa" - the weakened vowel sound which is uttered in place of a clear vowel sound.. E.g. in the word "illiterate", the first -e and the -a are not pronounced clearly but are weakened to a "schwa". It is as though these two vowels have been "squeezed out".

Are you sure the second one is not (biz/ness) instead of (birz/ness)?

Mmm, Hard to explain but I think it means it is almost 'extended' or said for longer. Business is pronounced like "Beers/ness", almost and really I think it means "bi/zi/ness" is wrong because you need to prolong or extend the 'i' in 'bi' to make it sound like beer/bir. I really hope this helps!

"Squeezed out" in this context means that the other syllables put such pressure on the syllable that it flew out of the word. They are being kind of funny about the phenomenon, but that is kind of what happens with the pronunciation of words over time. The syllables "biz" and "ness" are strong and over time pushed away the middle "i" syllable so that many people now pronounce the word like "bizness". Note: many people do pronounce the middle bit, but it sounds sort of like "bizeh-ness"

I think that "squeezed out syllables" is just a playful way of saying that in the example it seems like the syllable in the middle was pushed out by the other two syllables. Here are some ways that I would use the phrase: "The toothpaste was squeezed out from the tube." "The salesman squeezed out another five dollars from the customer."