Yes, everything you need to install this unit is included.

No problem at all, you can easily slip it off it's mount, although could you not also take your bike into work to save anything else going missing?

Yes, you can set dual tyre sizes

No, but there are alternative products that have a cadence monitor that I beliece can do that.

Unfortunately this computer does not provide cadence measurements.

Yes it should be OK. A 29" MTB wheel is the same size as a 700c road wheel (give or take a 1mm or 2). So if your tyre has a size marking similar to any of the 700c tryes listed in the instructions use that wheel size setting. If not measure the circumference of the outermost part of your front tyre (the part that touches the road surface). Get someone to help, mark the side wall of the tyre with a suitable marker or chalk & rotate the wheel so that this mark is at the bottom of the wheel (nearest the ground) now mark the ground with a suitable marker or chalk in line with the mark on the tyre, then roll the bike forwards in a straight line until the mark on the trye is back at the bottom of the wheel, now mark the ground again. Using a measuring tape, measure the distance between the two markings on the ground in mm's, this is your wheel size (eg. 2155) to set in the computer when you set it up.

Yes it does.

The sensor must be within 70cm of the computer so if you can mount it within this distance it should work.

Yes the total distance travelled is stored as you ride.

Unfortunately not, the distance to the rear wheel is too long for the wireless transmitter. You will need a rear wheel specific fitting computer such as the Cateye Strada Double Wireless computer.