I don't know if I can help you much, but that OEM starter might be for just the automatic transmission models even though it doesn't explicitly tell you - the aftermarket ones require special steps to be taken when installed in a manual tx.
To rule out the clutch switch, I'd get in the car and push in the clutch and then try it. If it works, then you'll have to bypass the clutch safety switch.
Since it is made for the 3, they must have taken the key transponder into account, like you said in your other thread. You can verify that it isn't the problem by simply inserting the key in the ignition (but don't turn it). If it works, then you know something is amiss with the transponder bypass somehow.
The fact that the thing acts like it wants to start it, but doesn't crank the engine makes me think it's the clutch switch. It makes sense that it just stops after because it tries to start, doesn't see an engine rpm signal, so it stops. It has no way of knowing if the engine is cranking, so it assumes it is and is just waiting for an rpm signal.
Did you have to add a hood switch? Most AM starters require an open in the hood switch circuit to work, but it might be backwards for the OEM starter and need a closed hood switch circuit - or it might need a 12v signal from the switch.
So, if you've hooked everything up right and checked the items above and it still won't work, there might be some other lockout mechanism added for manual txs to prevent people from doing what you are intending.
If it were me, I'd be trying to inject power into the ignition1 (computer and fuel pump) wire(s) and the starter wire, while having the transponder bypass engaged, while the hood switch is open (break the circuit), and clutch switch bypassed. These are the only steps you really need to get it to work. Door locks are unessential. The blower motor wire(s) will obviously need to be powered to make the heat work, but that is not essential either to have it start.