There are two different types of hyatt nights. Sign Up Nights (referred to as "SUN"s) and anniversary nights. The sign up nights are from when you sign up for the hyatt credit card. The anniversary night are given to you if you keep the credit card after the first year. You get one anniversary night every year. The sign up nights can be used for any hyatt hotel in the world on any date where a Standard Room is available. The anniversary nights can only be used in hyatt hotels categories 1-4 (Notable category 4 hyatt hotels: Hyatt regency mission bay, San Diego Ca. Andaz peninsula papagayo, Costa Rico.). Obviously the sign up nights are more valuable as they can be used in any hotel worldwide. The way somebody would book this night for you is they would put you as a second guest on the reservation. It is not recommended to combine nights between 3 different accounts or more. Or 2 accounts that none is yours. Obviously any reservation from a diamond account is more valuable since you will get the benefits as a second guest.
When you do the hyatt diamond challenge you get 4 suite upgrades. (For that matter a diamond member will get 4 suite upgrades every year). In order to complete the diamond challenge you must stay 12 nights in 60 days. There are people who will book you a room under their account and then use their diamond suite upgrade for your reservation. The reason why somebody would do this is simple. They want to complete the diamond challenge, therefore they will give you a diamond suite upgrade to get nights under their account and complete the challenge. Diamond suite upgrades CANNOT be transferred to another account.
Diamond suite upgrades can only be used for a cash or cash and points reservation. They cannot be combined with any free nights or full point nights. Diamond suite upgrades are subject to availability of the suite being available. You can transfer hyatt points between accounts, though you must fill out the form on hyatt's website. People have reported it taking under 24 hours for the points to be transferred.
C+P show up on the website, when available; and it will tell you if not available. And if a Diamond member were to book for you you'd get all the Diamond benefits listed on the Hyatt website.