Translation:My car is not as new as that of my friends.
No, the construct of the answer i.e. 'that of my friends.' includes 'friends' as a simple plural. The possesive is in 'that of'. If the translation had been 'My car is not as new as my friends'. ' then the posessive 'friends' ' would be correct (and more colloquial English.
"Il a une voiture plus/moins neuve que la mienne" and "sa voiture est plus/moins neuve que la mienne" mean exactly the same thing.
You will change "neuve" to "nouvelle" only if both parties bought a second-hand car.
Also, "une voiture récente" can be understood as a recently produced model of car, whether or not you bought it brand new or second-hand.
I'm sorry, that's not quite what I meant. I probably confused it by using the word attributive. Perhaps I should have said unmodified. What I am trying to ask is whether there is a feeling of 'recently' added when plus/moins are added or whether you can only use neuf/neuve to describe a recently bought firsthand car anyway.
"Une voiture neuve" is a recently bought, firsthand car. Now the subjective point is "recently" which is a personal judgment.
You can observe the cars parked along the curb in a street and say "il y a beaucoup de voitures neuves". It will mean that they look very recent to you but you have no way of knowing if they are firsthand or not.
If you look around in the car park under your own block of flats and say "il y a beaucoup de nouvelles voitures", it will mean that many new residents have settled in recently, irrespective of the cars' apparent or real age.
The sentence at the top of this page could be "ma voiture n'est pas aussi nouvelle que celle de mes amis" and the English translation would be the same. The difference is that with "neuve", the speaker is telling us he bought it firsthand.
With "nouvelle", he is telling us the model of his own car is less recent than his friends', but we don't know if he or his friends bought their cars firsthand.
For packaged goods, a pack of cereal you just bought will remain "neuf" until you open the box and pour the first serving. Yet on the pack, there may be a mention like "new recipe" = "nouvelle recette", that the manufacturer can legally advertise for 12 months.
Your sentence does not make sense because "friends'" with the apostrophe is short for "friends' car" and the verb cannot be "are".
Without the apostrophe and with "are", it does not make sense either because you would be comparing your car's age with your friends' ages.