Scratch org in salesforce dx

Hi ,

I have few qusetions regarding the salesforce dx :
1- In production how do we get the "dev hub" option , do we need to buy a license for this ?
2- Does Dev Hub is also available for sandboxes also (can we have a scratch org on the sandboxes ? )
3- How many active scratch orgs can we have for a prod or snadbox.

Thanks in advance !