Start with the instrument, not the player. A room that already has a decent piano in it makes this the cheapest good live music you can buy, because all you are hiring is a person and a stool. A room without one means the player brings a stage piano, a stand, a small amplifier and the time to carry all of it, and the quote will say so.
Melbourne complicates that in a specific way. So many of the city's function spaces are converted from something else, and a warehouse in Collingwood or a heritage room above a pub will have a piano that has not been touched by a tuner since it was installed. Ask the venue when it was last serviced before you assume the house instrument is a saving.
Top picks are the acts in this category in Melbourne, without a review, rating or premium ranking: all these sort keys are tied.
Some carry a weighted stage piano and a small amplifier, some will only play an acoustic instrument that is already there, and the two answers produce very different quotes. Ask in your first message and say what your venue has. A Melbourne player who regularly works rooms without an instrument will have a straight answer ready.
Hours, gear and travel, in that order. The cheapest version is a short set on a good house piano in the city, and the dearest is a long afternoon in the Yarra Valley or down the peninsula with an instrument in the back of the car. Compare the from-prices on this page and take the ones with no figure as an invitation to ask.
Usually yes, if you ask early enough. Send the actual recording you have in your head, not just the title, because arrangements vary wildly and a piano version of a pop song is a piece of work somebody has to write. Three or four weeks is plenty; three days is not.
A tuner costs a small share of what you are paying the player, and it rescues the whole sound. An out of tune upright makes a fine player sound amateur and there is nothing they can do about it on the day.
Narrow doors, a flight of stairs and no loading zone are normal in the inner north and around the city grid. Tell the player what the access looks like and they will plan for it rather than turning up and improvising.
Two hours of quiet playing under conversation is a mood, and a set people stop and listen to is a performance prepared quite differently. Say which one you want or you will get the other.