Let me go through these one by one:

Your original repair items:

Tranny flush: If it's an automatic transmission, maybe. If it's a manual, it should be a lifetime oil change. Also, is it really necessary to flush? A simple fluid change should be more than enough.
Fuel injection - Huh? The fuel is 'flushed' through every time you buy gas. If you have been buying cheap gas, I suppose that there could be injector clogging, but how did they diagnose this? Is the car running poorly? If not, throw some Chevron injector cleaner in there and you should be fine.
Coolant flush: OK, this is a good idea. Not sure if a full flush is needed.

Has this car had the brake fluid replaced? If not, that should be done every couple years.

This should be about $100 or less in fluids and no more than a couple hours labor. I don't know how they get $1200 out of this.



Your other items:


Replace failed component (Crankshaft position sensor o-ring
leaking)
<-- Good idea to replace this. it is a common source of leaks. This takes about 3-4 hours to access, but it's only a $7 part.

REPLACE OIL PAN GASKET (Oil pan gasket leaking)
<-- I doubt this is leaking. Most oil pan 'leaks' i've seen are due to the crank position sensor gasket. It drips oil down the front of the engine and the oil pan is wet because of this. The gasket costs $15 or so.

REPLACE LEAKING TSTAT (Found coolant leak)
<-- Probably a good idea to repair this. It's only an extra 30mins-1hr once you already have the front of the car off. I think it's around $20 for the part.

REPLACE LEAKING WATER PUMP, ADDITIONAL O-
RING, GREEN CHARGER GASKET AND COOLANT
(Found coolant leak)
<-- Should be repaired if it is actually confirmed to be leaking. Again, easy job when combined with the two above repairs.
If the water pump is really leaking, this is probably $200 or so in parts.

Replace lower control arm bushings (Found lower control
arm bushings seperated)
<-- Good idea to repair this. It takes about 2 hours. Around $100 for the new bushings?

REPLACE P/S COOLING FAN AND 5 AMP FUSE
(Binding)
<-- This is a 10 minute job. The part costs about $130 I believe.

Replace engine mount (Found engine mount
ruptured/leaking)
<-- less than 1 hour to replace. Good idea to repair this. The part is about $100 if I remember correctly.

Replace front strut mounts (Found worn out/noisy front strut
mounts)
<-- Hmm. I suppose it is possible that these need replacing. This is a 1hr job.
The parts cost around $80, but I don't remember if that is each strut or for the pair.


Even adding up all of these jobs, the labor should be not more than 10-12 hours, but they probably are charging the book hours for each of these jobs standing on their own. If we charge these jobs as if they were done separately, it could be 18-20 hours of labor or more.

An independent shop should quote around $1000 labor and less than $1000 in parts. While it is questionable whether all of these jobs need to be urgently done, all of the engine leak and control arm work can be combined to save labor.

I am surprised to see all of these items on a car with 27,000 miles. Has this car seen 99% city driving?

 

Sounds almost like the dealer searched NAM for "gen1 mini problems", then they try to get a person to fix them all....
Kinda unusual to have all the common issues on the same car....at the same time....things that make you say huh....

My guess is a few things might have been needed, but guessing from the low miles, the car sat....some of the seal shrunk...so when the op started to drive, they started to weap...so they look lke they are leaking.....bet a few miles of fresh oil, and the oil leakes will be ok...
Most of the stuff, while common, is uncommon till 50k plus miles....but an indepenant shop is imo a strong suggestion for any gen1 mini!!
Flushes can ne more of a problem than a help imo unless there is a contamant....a drain and fill on most things should be fine....a suggestion for a tranny flush on a manual....lol...unless one does lot of gear grinding in 27k, hard to not laugh at that one.....

 

The jcw kit has more to it than that....
the parts you are listing was to "upgrade" a pre 2005 200 hp jcw to a 2005+ jcw210 hp kit....the rest of the kit (the ported head, hower mildly done was part of the kit, and was the main reason for the $$ of the kit...pree 2005cars also got a coated sc, standared on 2005+ cars, with a pulley that was about a 12% reduction....
not sure how many kits are left around....for the same $$, aftermarket gets most of the hp for less $, most folks got the jcw kit to matain their warrenty, and to get a pre modded car....but a mini lent itself to making a car that was 90% of a jcw or even better for less $. Most dealers should have a gen1 car guy around to explain to you kit avalibility, etc....but my guess is the newer dealerships have never sold gen1 cars....or workef on them much....