Hi welcome,
Firstly you say it will open but won't lock with the fob. Does it try to lock? Ie clunks and goes down but almost straight away pops back up?
If thats the case its probably the door lock solaniod gone, fairly common on early facelift models. Before i discovered this place it cost me around £80 at a dealer to get it fixed. However someone here should be able to offer more advice on doing it yourself much cheaper!
Second problem you air-con... you say it won't turn on. Do this little test to establish if the compressor is working:
Start the car, and press the "OFF" button on the climate dash.
Now wait say 5/10 seconds.
With your drivers door open, (you need to hear the engine) press "AUTO".
Now this should do several things:
1) Revs should increase by around 100 rpm or so, you should see the needle rise slightly
2) The engine will sound throatier because its running higher RPM
3) You should hear a slight click.
If you get the above, good news the compressor is running. If not, then your compressor has problems and could prove costly.
However if you do get an increase in revs then there is probably sometime else wrong, however my info on this area is limited so someone else will be along soon....