diesel range rover problem?

my mate has just purchased a 1998 r reg 2.5 dse range rover, has a couple of problems firsty it kepps coming up key fob battery low or somthing like wise he is going to chane batteries and hopefully this is problem but main issue is when started from cold the other day it came up alternator fault and the revs went high by themselves also it has dangerously low power next to nothing when cold and will hardly accelerate then when warn all is fine any advice would be very very much appreciated many thanks.

high revving and alternator fault can be caused by crankshaft sensor check to see if rev counter is working when it revs high if it is then sensor should be ok dont automatically change the sensor though mine was just a broken wire if u do need a sensor L.R are £112 eurocarparts for a bmw 525td £54, mine used to be useless when cold but i never got chance to find out why as a valve head decided to part company with the stem and wrote the engine off,also try getting it plugged in on a diagnostic reader.