Help Mini Cooper problems!

1 year ago I purchased a Mini Cooper 2010. It had
38,000 miles on it. I had to replace the brakes and
spark plugs after 10,000 miles of driving which was
fine. But now I am having a bunch of other issues.
First my car completely died and would not turn on.
Turns out the key had died or shorted so I had to
get that replaced for 280. Then a few months back
my check engine light went on and then went off a
day later. Then a few weeks goes by and I am
driving in a residential. I come to a stop and the car
dies. It started up again immediately. Went and got
another oil change which my service advisor at Mini
suggested. That same night I was parked and then
put my car in reverse the car shook a little as I
moved backwards and then died again. The check
engine light went on an off for a few weeks. I  
Schedualed an appointment at the dealership but
the check engine light had gone off and the advisor
warned that without the light on they can only
guess what the problem might be. About 2 months
went by and the car has been perfectly fine minus
the key issue. Then a week ago my engine
temperature warning came on. Checked my coolant
and it was empty. Filled it up and warning went
away. 4 days later warning came back and the
coolant tank was empty again. Looks like I have a
crack somewhere because I saw the coolant
evaporating from the drivers side of the hood. So I
am taking it in Tuesday. On top of that my car check
engine light came on again and the car shook a little
when I went into reverse. Any idea what the
problem might be ?