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Certainly this would depend on the varieties that you are propagating.

Isn't it the dead of winter now in southern Australia? You may have answered your own question. It depends on the climate, but also on the type of vegetables you are growing and your soil and water management program.

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-9-10-11/zone-9-winter-vegetables.htm

This link has a list of plants for you.

https://aggie-horticulture.tamu.edu/ornamental/a-reference-guide-to-plant-care-handling-and-merchandising/propagating-foliage-flowering-plants/

It can, but this is not as likely to happen. Usually, the distal end will die up to the graft point.

This depends on the vegetable. Cool season veggies should be ok to start now, but I would wait until about 6 weeks before the last frost date in your area to start any warmer season vegetables. This article will give you some useful information: https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-9-10-11/zone-9-vegetable-planting-guide.htm

Roots grown in water are different from roots grown in soil. Water-grown roots tend to be very fragile. To get them acclimated to soil, it is best to introduce the roots gradually to soil. For example, you can start with a 50/50 mix of water and soil and gently add your plant. Every day or two, add more soil into the container till all the water is absorbed.