If you can make calls, then the phone is working properly.
Data can be disabled on the carriers end, so perhaps whoever sold you the phone had the data turned off to reduce monthly fees.
As for apps; cell phones nowdays have parental controls just like your home PC. Perhaps the previous owner had the apps locked to prevent unauthorized people from using them.
For both of the above, you will need to contact the person you purchased the phone from and ask for assistance. If it was under contract, and the contract has since been signed over to yourself, you should be able to get this assistance from T-Mobile.