Is it true that the synthetic human growth hormone really help you grow? |

Yes. It seems to be true but is expensive and as with all treatments it can come with some risk at 37 years old all of your growth in height is at an end so it will not change that.
Depends. It is not like gasoline you put in your car. To grow taller your growth centers must be open and ready for HGH to work. If you are a short 10 yo with HGH deficiency, this can help. However growth centers close in females around 15-17 and males 16-18. Once closed, they do not reopen. The $ 10K/yr + cost would not be a good investment for someone your age.
Yes, if growth plate. Still open. It's very similar in structure to the natural version.