I have Cooper S 2009.

1. Do I have to replace the sensor once I replace the front brakes?
2. How do I know if I need to replace just the pads or the rotor as well? (In Mini dealer they told me that I need to replace both pads and rotors)

 

You have to replace the sensor once it has been triggered, which is somewhere around a few hundred miles to go on the service warning.

In my experience, when you remove the sensor from old brake pads, the metal clip that holds the sensor in the pad goes missing, so even an un-triggered sensor may need to be replaced because it won't hold in a new pad - I suggest you get one anyway, so you've got it if you need it.

The tests for the discs are:
(1) Is their remaining thickness greater than the minimum, which is cast on to the disc near the hub. You need vernier callipers or a micrometer to measure this accurately enough.
(2) Is the surface of the disc free from grooves and doesn't have a lip at the edge. This is a judgement call, so not that easy. If you drag your fingernail across the disc surface and it bounces in and out of grooves, it's time to replace the discs, I'd say.

You could always photograph your discs through the wheel spokes and post them here, to see what advice you get.

 

No.
The sensor is nothing but a wire loop with 12V running through it, enclosed in a plastic plug to fit into a brake pad. As the pad wears, the last 2/32nds wear through the sensor wire loop. Once the circuit is broken, pad wear light goes on. THEN you need to replace the sensor. Otherwise, you can gently pry it out of the old pad, and put into the new. Or tie it around the strut tower if you are capable of monitoring brake pad wear with your eyes

Like Angib mentioned - you measure the thickness of the rotor the similar to how you measure the remaining brake pad material before you decide it's time to replace either.

For example, R56 front rotor is 294X22 mm, with MIN thickness of 19mm. So there really isn't THAT much rotor material to work with! If the previous pad set took you down from 22mm to 20mm, you may need to replace your current set of rotors (always work on them in pair: front and rear) before the new set of pads is likely to be worn off.
If you are down to only 21.0 or 21.5mm, you know your new set of pads will likely live through the current rotors just fine.

Dealers like to swap both at once, as they book you in for double the book rate of both jobs, even though they save considerable time on the rotors once pads are off.

I would not worry about grooves or the lip.
Grooves are just a result of having a rock caught between the pad and the rotor. Happens all the time with no ill effect. Some rotors come with pre-cut grooves as an extra $$ feature.
w.r.t. the lip - it's normal and nothing to worry about. The pads are always smaller than the rotor, and never extend beyond the edge of the rotor. The grooves form in the areas where the pad doesn't make contact with the rotor. The new pad will be the same size, and wont touch those areas either. Lips are normal.

a

 

Whatever you do try doing it your self if at all possible. I just went through the process. If you can follow instructions from youtube videos you'll be good to go. Only need a small assortment of tools. The dealer wanted to charge me $300+ just to change the pads on the rear brakes. I paid about $400-$500 for all pads and all rotors and just did it myself.