I recall some time ago Siwastaja mentioned in this post that the suppress diode/tvs should be close to the fet and not on the load so I've been following that and that's why I put that tvs across fet drain and source. Hope I got that right... Maybe in this case it doesn't matter as the wires between load and fet are short so both approaches are ok.
It's still in the wrong place, in the schematic. It needs to be in parallel with load, not parallel with the MOSFET; the post you refer to talks about
layout; it should be close to the MOSFET. Placement and circuit are two different things. Paralleling a freewheeling diode with the MOSFET does not do much because the MOSFET already has built-in parasitic body diode. You want to provide a path for the current which still goes through the load after the MOSFET goes open-circuit, and the only place to offer this path is in parallel with the load.
If the load (in this case, piezo) is driven such that off-time is always significant, then any diode type is OK (forward recovery time matters; but it's good enough with nearly any diode type). On the other hand, if you drive the MOSFET back on quickly (e.g., because you do PWM), then you need to use a diode type with fast reverse recovery, or no reverse recovery at all, schottky is the usual choice then. A "normal" slow Si diode would be still conducting due to slow reverse recovery and cause significant short-circuit current through the diode+MOSFET series connection.
#1 for even slightly inductive loads is to add the freewheeling diode, and having it physically close to the MOSFET is right because it then also freewheels the parasitic inductance from the wiring going to the load. Always try this first, remove the problem where it's generated. After that, if you still have ringing, which is now caused by the parasitic inductance of your switching loop (loop formed by your closest DC bus capacitor, MOSFET and the freewheeling diode all in series) forming a "tank" circuit with Cds of the MOSFET (or C of the diode), then you can add RC snubber(s), across the MOSFET and across the diode.