Many thanks. Very interesting.
Cold start:
1. This time you do have a bias voltage. But we cannot dismiss the fact that it was zero on your Motor stopped for throttle logfile.
2. Nearly 3 minutes to go into closed loop? I don't know - it might be normal for the Mini, I doubt it - that seems very slow.
3. Look at STFT: it starts off good, especially between 4 - 5 mins. It's close to zero and narrow banded. But look how it drifts dowm after 8 mins and starts to fluctuate over a much wider range. This is really interesting. it means the mixture appears to get richer as the car warms up. The purge valve is not commanded open during this time. So this makes me think that Leopold's suggestion (to me in an email) may be right: could the purge valve be stuck open?
4. The sensor is switching about 20 times a minute at idle. On your 2500 rpm logfile it was much faster, as you would perhaps expect. But given it takes nearly 3 mins to go into closed loop and this low switching at idle, you really ought to check the oxygen sensor heater is working. When you disconnect the oxygen sensor the 2 wires with the same colour (on the sensor side of the connection) are the heater wires. If you measure the resistance you should get perhaps less than 10 Ohms; whatever it is, it must not be OL (open circuit) - be careful, do not damage the pins or females in the connector when testing When I first looked at your lambda graph it looked - to me - as if your heater was working, but that's pure speculation. There is no substitute for properly testing it.
Idle without Carbon Canister
Again interesting.
1. No sign of any change in maifold pressure or RPM when you take it oof or put it back. Interesting, perhaps too low an airflow in, still a bit odd.
2. On the Full Trip scale, look how STFT starts to climb after you took the pipe off - this means MEMS has reduced the amount of fuel it is taking away. In other words, the mixture is getting leaner (less rich with time). Now look what happens when you put the pipe back:STFT shows the mixture slowly gets richer over the next 3 minutes. So something was going on during that test when you disconnected the canister. Again, this suggests that possibly the purge valve might be stuck open and that further investigatioin to check this is required. Whatever it is, the cahnge was not instantaaneous as you might expect, especially pulling it off.
So, if at all possible:
a. Test the resistance of the 02 sensor heater. I'm not yet convinced the 02 sensor circuit is perfect.
b. Take off that vacuum pipe to the carbon cannister again and this time seal it up with tape or block it and let's see some logfiles of your driving the car with the pipe sealed and not connected to the canister I would also leave that pipe blocked for the moment and see if the car behaves any better over the next few days. But remember that your oil may contribute to making things slightly richer than they should be. Again start all logfiles with the ignition on but the engine stopped, and when you finish, stop the engine and put the ignition back on for a minute and then stop logging. I'm still thinking about that lack of bias voltage on your throttle ogfile.
And what about coolant - are you getting any coolant loss? Do you have to keep topping it up, even by a small amount?