If you were still the registered keeper, then it would have been your duty to tax the vehicle which means that you may be fined if the car did not have valid tax. However if you can prove that you were in the middle of changing ownership, then maybe the fine can be billed to your friend's name.
Regarding your friend speeding in your car, if you can prove that you were not driving the car, then you will not get any points on your licence. The speeding reminder will be sent to you if you're still the registered keeper but they will ask you to confirm whether you were the one they caught speeding in the car. You just have to say it was your friend and give them some proof so that your friend is fined for speeding instead of you and points applied to her licence rather than yours.
If you require more help, then it is best if you seek advice from a professional motoring solicitor.