Q1. If you're flying coach, then see your point halved on Cathay's programme and on Qantas' programme by 30% (QF only awards 70% of miles in disounted economy). QF also is the only programme that charges to join. A$50. Unless you live in Europe, then it's free. But then, you can only accumulate mileage if you fly in J or F class. BA might be it for you.

Q2. And no, you do not need one segment on the home airline to qualify. But you do need 4 segments in order to retain the elite status, if any. Otherwise, it's fine as it is.