Welcome to the T&TH message board and to turkey hunting. I've been chasing those big red headed birds for a long time now but certainly don't have all the answers. I will however try to answer, as best I can, some of your questions.
In most areas where I've hunted, there are owls, crows, dogs, coyotes, etc. that are very active early in the morning. Many times a turkey will respond to one of those "natural" sounds and gobble. If he does not, and I reasonably believe there is a gobbler in the area, I may try something different, like a pileated woodpecker call. I may try that from my original spot and may try it after I've moved to another spot, if moving is what I choose to do.
There is really no "right amount or wrong amount" of time to wait in one spot. In my experience however, longer is usually better than shorter. A turkey is not on a clock. He may decide to come to where you are but he may take a lot of time to do that. By moving, he may well see you and decide another place is better than where you are.
Many times roost trees are located by accident. We just stumble across them as we're making our way through the woods. We can up our odds however by looking for likely trees, with good limbs, half-way up hills and with clear spaces where a turkey could land, etc.
If you find a number of turkey scratchings, you may be able to follow those backward until you find a source, maybe a roost tree.
I've also found roost trees by just sitting in the woods at fly up/fly down time and listening. When I hear more than one bird fly up/fly down (I'm lucky) and I may have also found a roost tree.
Turkeys may stay in an area for a long time if there is food, shelter and water...and they are not disturbed, or they may just wander away. That's what makes this sport such a challenge.
My best advice is to enjoy the hunt. I'd also suggest that you read the article "Good End of Season Advice"
You may find it helpful.