So, reverse engineering this...
From the schematic, we can at least tell that your air handler has no heat strips, just a fan and a direct-expansion (DX, aka evaporator or indoor) coil in it. As a result of this, and the fact that your heat pump appears to be a fairly simple unit with only a reversing valve and a compressor contactor, this is actually not a terribly complicated system to reverse-engineer.
From the wiring photo you showed, we can tell that the current thermostat is wired using the black, red, orange, and white wires. If at all possible, you'll want to strip back a bit more jacket, extract enough blue wire from it to strip and wirenut a connection onto, and then use a jumper wire (a piece of 18AWG TFFN will do) to attach that stripped blue end to the existing junction of the thick yellow wire from the transformer (the whatzit in the middle with wires coming out both sides), the thick red wire going to the fan relay (black lump at the top right), and the thin red wire going off to the heat pump outdoor unit.
With that done, we can tackle the rest of the wires. We know the red wire to the thermostat is R because it's connected to the other yellow wire to the transformer, first off. From there, we can look at the fan relay and trace its white wire over to the black wire from your thermostat, which makes that black wire your G wire. This leaves your white and orange wires, which both go off to the heat pump outdoor unit. Conventionally, orange is used for the reversing valve which determines whether your heat pump is in heating or cooling mode, so that's your O (or O/B) wire, and that leaves the white wire as the Y wire that turns the heat pump compressor on.
So, in short, your wire designations go as follows:
- Red - R/Rc
- Black - G
- White - Y
- Orange - O/B
- and Blue -- the C wire we just added
Your W/W1/E/AUX terminal will remain unconnected, unless it's hooked up to a different system altogether. Also, you'll want to make sure that the O/B setting on your thermostat is set for O when you first program it, so that your thermostat energizes the orange wire when cooling and leaves it de-energized for heating. (Unless you have a Rheem or Ruud outdoor unit that is, where you'll need to set the O/B setting to B to begin with instead.)
If things don't quite work right
If your system heats when calling for cooling and cools when calling for heating, then you'll need to flip the O/B setting on your thermostat. (You'll only likely need to do this if your outdoor unit is a Rheem or Ruud, though -- they're the only units that commonly do things the other way around.) If your system will not change over (i.e. heats when calling for both heating and cooling, or cools when calling for both heating and cooling), then your orange wire will be your Y wire and your white wire will be your O/B wire in that case.