I can't help with the second one but I know the forward O2 sensor should be the NGK 25648 or OEM... Which is the same sensor at twice the price. I had a brand new Bosch sensor installed prior to taking ownership of my 2004 R53 and it would kick the code after 3 or 4 starts. Read up online and found that the car is really finicky about he forward O2 sensor and that this is the one to get. Changed it out and no more code! Click Here
So, O2 sensors do go out. That's possible. It's strange that it happened right after the other work.
The O2 sensors are part number 8 on this diagram. http://www.realoem.com/bmw/enUS/showparts?id=RE33-USA-08-2004-R53-Mini-Cooper_S&diagId=18_0475 There's 2 of them. One before the cat (the one on the left), called the "upstream O2 sensor" and one after the cat (the one on the right) called the "downstream O2 Sensor". The upstream one is important, because it controls how the engine behaves. The downstream one is only there to make sure the cat is working, so it can throw errors if you emissions are out of whack.
Also, be aware that shops have a high mark-up on parts. I don't know UK prices, so I'll do it with the US prices. So for example, the part lists for $215 USD. If you go to the shop, they'll charge you that much for the part. Parts are quite silly at times. According to Some smart people NGK makes the sensors, that they sell to Boche, which they sell to BMW. You can find the NGK version of the sensor for $99 Car parts are silly. The dealer gets a moderate amount of the markup on the part, but BMW takes a fair bit as well. Even if they give you the labor for free, they going to charge you 215 for the part, which they probably paid bmw 150-170 for.
That said, I have no problem with the dealership making money, I just want the process to be more transparent then it is. They need to make 200+/hr to cover all of their costs (insurance, tools, rent, labor, etc) It sounds like they are overall trying to treat you fairly.
So what to do depends on your situation and your handiness level. I'd start by checking to make sure the O2 sensors are actually plugged in since work was done recently. Perhaps in some of the work it got unplugged? The cables have a white jacket (that'll be covered in grime) that will run up from your exhaust up towards your computer, and plug in. Inspect both wires, make sure they don't appear to be damaged, and then make sure the connectors are on tight. I can probably find photos if you can't find the wires.
If you've got more time then money, replacing an O2 sensor isn't hard. You'll need to buy some tools, so your first few projects you'll only break even, but you'll have tools for next time your car needs some love. Or the car after your current mini... If you want to go down this route, I can provide info on how to do the swap.
Now the other half of the question of if it's related... If the O2 sensor itself went out, that happens, and that's not fishy. But the question is what error are you actually getting back from the computer. There's several different errors that can come back. One of the errors say "The sensor is reporting strange numbers! It's probably broken!" One says "The sensor isn't responding at all! It's unplugged or broken!" It depends on which one you're getting. The first one they can't cause at all really, the second could happen if they forgot to plug something in. If you're getting the disconnected error, you said they were working on your fan's wiring. It depends on what they did if it's possibly related to the fan wiring. If they were working on the fusebox wiring, or the ECU wiring, then they could have caused it.
In the US, most auto part stores will read the codes out of your car, and knowing the code number, I can tell you which sensor is broken, and which message it's saying. You can also buy a cheap code reader for $20, or a good one for about $60.
One choice you have is you can tell the dealership that you want your car back for a few days for some reason, and you'll bring it back. You can get the codes read, make sure it matches up, do a quick visual inspection, and know what's going on, and then decide if you want to take it back to the dealer or not for the rest of the repairs. Or you can take it to an independent shop as well. O2 sensors aren't hard to do, so any vaguely competent mechanic should do it correctly. It'll take them more time to figure out how to unplug the connector then anything else, probably.
The other choice you might go for is tell the "Sure, I know O2 sensors go out. If replacing the O2 sensor fixes it, sure, I'll pay for it. A part on my car wore out at the same time. Otherwise, if it's not the sensor, it's a wiring issue. And you just dug into the wiring of my fan, and you possible you broke some of the O2 sensor wiring, and I expect that fixed for free. And I shouldn't have to pay for the incorrectly replace O2 sensor." It kinda depends on which error is coming from the sensor though, and if the problem with your fan was in your fusebox and/or ECU.