bmw x5 2005 electrical problem

[skrewcop]

hi i recently bought a 2005 bmw x5 4.4i xdrive and when i start it in the cold canadian mornings(or evenings, here it's always cold lol) the 'trans failsafe prog' error shows up and the ABS light comes on and off and when it's on, the car loses power: the interior lights go a bit dimmer, the NAV system shuts down, the headlights switch off and so on...After like 20 mins if i leave the engine running, the abs light stops from coming on and off and everything comes back to normal...yesterday i even had an error saying something about suspension i cant remember what. Now the guy who sold it to me said he had replaced the battery and alternator a week before i bought it and he put them on himself. could this be because he did not do the job properly? i love this car so much and i want to fix it. thanks