Will I keep growing or am I done?!

Your normal body development (height, body mass, muscle, but not genitals) continue growing for up to 4 years after puberty ends. For most guys this is around the age of 20, assuming you had a normal puberty that finished at around the age of 15 or 16.
How tall you are is hereditary and the clinical formulae for the prediction of a boy's height is either to double his height on his second birthday, or to half the sum of his parents' heights and add two and a half inches. This is accurate in 80% of cases, so there are exceptions because genetics can throw-back to previous generations.
See the link below for full clinical details on adolescent development.

http://www.usc.edu/student-affairs/Healt…

This depends on what you do, such as your exercise and eating habits. You will find that you will begin developing a more muscular body, but as for height, less of these "height" hormones are used as you continue to age. You cannot compare with your cousin as he is not the son/daughter of your own mother and father and is therefore not directly related to you. If you play sports and stretch a lot (yoga, gymnastics, or a running activity such as soccer) your muscles might be able to go that extra inch to your height, but don't expect a great deal more. 6'O is decently tall for 16 year old males what with how kids are eating these days; sodas, burgers, AKA garbage that hardly gives ANY nutritional value needed to serve the body.

Nobody knows, Bubba.
Genetics rule - you cannot re-program genetics.
You will not finish puberty until at least age 21 - or later.
More growth could be headed your way - nobody knows for sure.
You just need to be patient & wait to see what all develops.
Don't worry about stuff you have no control over.

Maybe, maybe not. Can't tell, no one can. Relatives give you a general idea, but then again ive got a uncle whose around 6'7" and im like 5'8". Give it a bit, ten bucks says you'll get taller, maybe not six ft but taller....