Its one of the hazards of buying used I suppose, you can get a fantastic bargain, or you could get a load of trouble, all depends how its been looked after in its past life.
Some folk never ever lift the bonnet to check anything, or clean it until its due to go then they spend a mad weekend polishing it so they can say very good condition well looked after etc etc, ha. Thats the sort of car you dont want, but of course you dont know half the time.
You never know if the faults you have are the very reason the last person got rid of it for, or it could be just sods law and its all going wrong by chance, lucky you have warranty so you can hopefully get it all sorted, should be a good car once it is, my niece bought a 2003 Mini One and has never has a thing go wrong in 80000 miles, she loves it and is buying another on the strength later this year.
Im about to get my first, a new JCW and Im looking forwards to it.