Hsa Contributions

If an an independent under 26 and my parents claim me on their HDHP insurance, can I still open up an HSA and contribute?

 

Also, if they have a family HDPD, can I contribute $7,300 instead of $3,650??

 

finally, is it better for me to open up an HSA with my employer (I am under my parents plan) or should I open an account up myself? (Would the money I put in still be tax free)

 

THANK YOU