No, connecting an outdoor shower to your potable water supply or sewer drain is licensed plumbing work in Victoria. The only DIY-legal scenario is a fully temporary garden-hose attachment with no permanent fixtures and no drain, which most people don't actually want.
Both work. A cold-only outdoor shower runs off the existing garden tap supply with a tempering valve if needed. A hot-and-cold outdoor shower needs an extended hot water line from the existing system, which is more work but gives a usable year-round shower. We quote both at scoping so you can compare.
It depends on what you're washing off. Pure rinse water from beach or pool use can typically discharge to a stormwater point or a rubble pit. Soap, shampoo, or any greywater discharge must connect to the sewer, which is a bigger plumbing job. Council bylaws sometimes restrict the discharge point, we check at scoping.
Yes, any new water or sewer connection ends with a BPC Compliance Certificate. The certificate matters at sale settlement, because outdoor shower drains that bypass the sewer can show up on a building inspection.