Two layers of 5 8 plywood at least then use cement board.
Can hardboard be place on top of vinyl tiles.
Fill low spots on the floor with patching compound applied with a putty knife.
Surely ply has better moisture resistance.
It is not a good idea to lay ceramic or stone tiles on suspended upper floors unless you are sure that the joists can carry the extra weight consult a structural engineer for this.
4 loose lay more boards up down and across the room.
I believe you want to be tiling on something like cement board or ditra not directly over plywood.
2 loose lay the first board over the centre with its long edges at 90 degrees to the floorboards.
Hardboard is a very poor poor product to use for preping a subfloor.
How to 4 laying hardboard and plywood 1 use a chalk line to mark two lines at 90 degree angles to each other across the centre of the room f2.
3 adjust it so that the edges do not correspond with the gaps between the floorboards.
To properly install a new tile surface you should remove the existing vinyl tile grind down as much of the old tile adhesive as possible and then apply the leveling compound to smooth out the surface for the new tile.
Stir ready to use floor patching compound with a paint stirring stick.
If your flooring is already thick enough needs to be stable to prevent cracking later.