Ask an Property Solicitor. Get an Answer ASAP.
I cannot see you have provided a copy of your lease. If you would still like me to take a look, I will happily do so if you can upload a copy here.
Generally, it does depend on what is stated in your lease as to who is responsible for repairs.
If there is no parking space mentioned in your lease then it is unlikely that you will have one allocated. If you speak with the management company, they may be able to tell you how to proceed to purchase one.
I hope this clarifies somewhat.