My short answer would be "yes, absolutely". Hyatt is the best program.
But...
I looked at your questions and realized that our interests are different.
I'm more interested in the hotels than the treatment I receive as a Diamond. And, for my dollar and desires, Hyatt dominates in every category: Hyatt Place, Summerfield Suites, Hyatt Regency and up. For me, all the perks in the world don't matter much if the hotel facilities or service are shoddy.
1) How often are you giving lounge access?
Reliably in the full-service hotels that have them; otherwise a breakfast voucher for coffee/pastry/juice. But I never go. I'm health conscious and prefer to make my own food/avoid typical lounge fare. My work weeks are often 100+ hours, so I don't hang around the lounge.
2) How often are you giving upgrades to club room?
Again, reliably. I'm not always certain that I can identify the difference.
3) How often are you giving upgrades to suites?
So far, ten years as a Diamond, never. That said, I spend a fair amount of times in Hyatt Places. And in the full-service lines, I really don't care, so I don't ask.
4) Is Hyatt Diamond better than SPG Platinum and Hilton Diamond?
It depends. I think SPG is nearly as good on the promos, but when faster free nights comes around (or whatever they call it), my preference has to be Gold Passport.
5) How good is this program if you are staying on travel agency rates (expedia, priceline) - Still giving lounge/upgrade and/or points?
No experience here.