The duration of the fixed-rate bond is approximately 75% of the maturity - is this a given fact like duration of a floating bond is 0.5 * coupon frequency?

Yes. If they don’t give you either you need to use those shortcuts, but floating rate is (1/annual reset frequency)*0.5. So a quarterly floating rate bond has a duration of (1/4)*0.5.

Semi-annual floating rate duration = 0.25

Quarterly floating rate duration = 0.125

No, it will be given to you in the question.

If it is not given in the question, I would personally assume it because that is how every question in the text has been that I’ve come across.

The generalformula is:

duration of swap = 0.5/(#pmts per year) - k*(maturity)

here, k=0.75

thanks guys!