It would help if we had the engine codes and the two ecu types (EDC15/16, Med7/9 ect) and the fault codes that are present but here goes:
It sounds like the engine was swapped complete with the correct engine wiring loom for that engine and the correct ecu for that engine has then been unlocked (had the immobiliser removed). If this is correct there shouldn’t be many fault codes concerning the running of the engine. Any fault codes will probably be due to lack of comms with missing modules/ecus that the donor car had that the current car hasn’t.
There may also be fault codes in other ecus/modules due to not communicating with the engine ecu properly.
VW engine conversions are fairly common practice (in UK and Europe anyway). There are two options depending on what codes you have. Get a decent tuner to delete the present fault codes in the engine ecu, I say decent tuner because there are many ways to delete fault codes in the firmware file and you don’t want to end up with the ecu not reporting any fault at all as damage may occur if you don’t know about them and diagnosing faults would be a nightmare.
Get a tuner or decent auto electrician to ‘virginise’ the engine ecu and then reprogram it with VAG-com. This may or may not be possible depending on ecu and engine numbers.
So for anyone with experience with VAG vehicles and ecu tuning this is a very easy task if you know your way around the flash file.
Update based on your additional info:
Using the clocks and additional modules from the donor vehicle is a really unprofessional way to get the engine running correctly. This is really a simple task for any decent tuner or specialist auto-electrician. The engine ecu just needs reprogramming and unlocking properly.
17524 Bank1- Sensor 1, Heater circuit, Open circuit (P1631)
17526 Bank1 Sensor 2 Heater circuit, Open circuit (P1118)
Both of these should be easy to rectify, you need to test the wiring and confirm if the O2 sensors from the donor vehicle have been used or are the same. The fact that both sensors have faults seems to suggest that the wrong sensors are being used or there is a missing live somewhere.
18014 Rough road spec engine Torque ABS-ECU, electrical malfunction in circuit (P1606)
18020 Engine control module, incorrect coding (P1612)
This is because the ecu is coded for auto rather than manual. This can be done in two ways, use VAG-com or similar high level diagnostics to reprogram the ECU to manual and while your at it you maybe able to reprogram it to the ABS and other modules in the vehicle, you may need to have the ECU 'virginised' first. Or have the ECU reprogrammed through the flash file by the tuner or person who is unlocking or tuning the ECU.
18039-Accelerator position sensor G79, signal too high (P1631)
Should be as simple as the wrong accelerator pedal. Confirm that the connectors are pin compatible and then swap the pedal.
18088 Reset-resistant limp home (P1680)
This is due to the incorrectly coded ECU. This is usually a sign that the immobiliser has been poorly disabled and they haven't corrected the checksum. But it also appears when the ecu is incorrectly coded which yours is, so I would have the ECU coded or tuned first as this code will then probably disappear.
So you really have nothing to worry about, you need to do the following in this order:
Check the O2 sensors & wiring, swap the sensors if necessary.
Check the pin compatibly of the accelerator pedals and swap them.
Have the ECU reprogrammed either through VAG-com or my preferred option would be to have a professional ECU tuner swap the memory contents to a manual file with the immobiliser disabled, then delete the relevant DTCs from the flash file and tune it at the same time.
I repeat, do not use the instrument cluster (clocks) or other modules from the donor car, it really is just a case of programming the correct ECU for your engine and ensuring that the correct loom, O2 and accelerator pedals are being used.
