Oh, that is too funny to see the turkey trying to fit! The duck looks like a muscovy? That is what I keep too...
There are multiple questions in your post - I'll try to address them all.
Broodies are a strange bunch. All they want to do is sit - they don't care what they are sitting on as long as it is vaguely egg shaped. I've heard of a broody hen who valiantly tried to hatch walnuts for many weeks. They don't feel proprietary about "their" eggs, and don't have any bond to any particular egg, whether they've been sitting on it for a day or a month. It is not at all unusual for them to get up to take their broody break, then return to a different nest to sit. As long as they have at least one egg under them, they're happy.
What I try to do, to avoid having a hen sit on an egg and then abandon it for another nest the day before its due to hatch, is to segregate each broody into a separate area. That doesn't mean you have to have a zillion coops sitting around - it can be as simple as taking a piece of chicken wire and stretching it across a corner of the coop. Place the hen into the segregated area with her nest and the eggs, add a small feeder and waterer (preferably far enough away that she has to actually step off the nest to reach it) and voila. Now, unfortunately, I've made that sound simpler than it is because, having minds of their own, sometimes they don't want to move to the new location. I've had the best success moving them at night. Even then, sometimes when they wake up next morning and don't recognize their surroundings, they'll jump off the nest and pace looking for a way out. I've had to practice "tough love" a few times, and lock them into the new nest until they've accepted it as their own. Usually a few hours to a day is all it takes. Just make sure to remove the barricade that is keeping her in her nest a couple of times a day to let her out to potty, eat and drink, and once she has done all three, place her back on the nest and replace the barricade. Once she seems to have accepted the new nest, remove the barricade permanently so she has free choice about when to take future breaks.
If your duck is anything like mine, she'll make a fuss and get a little vocal (my broody ducks sound like squeaky toys) when you try to reach under her to get eggs, but won't take it to the next level.
Quote: Tough to say as there are so many factors. The warmer your ambient temperature, the longer they can survive. It is perfectly normal for the hen to leave the nest for 20-30 minutes to potty, eat and drink, and leave the eggs to cool. A dedicated broody will race around to take her break, rushing to get back to her nest, as nature tells her not to let them cool for too long (as said above, she doesn't always return to the right nest but generally she is in a hurry to get back to "a" nest). I've also had a power outage while running incubators, and even with the power off for several hours, the chicks hatched no worries. So - there is a period they can survive. Our summers where I live now are so hot we have temps in the mid to high 30's and 40's celcius for weeks at a time. Obviously, a broody hen can leave the nest far longer in mid-summer than she can in early spring when temps are far cooler. Also, the closer a chick is to hatching, the longer the eggs can cool, as the chick starts to be able to regulate its own temperature somewhat, in preparation for life on the outside.
Candling is definitely your first step. I'd be concerned about eggs incubated for 35 days that have not yet hatched. It is possible the tom is not doing his job and the eggs were never fertile, or that she did return to the wrong nest one too many times and hasn't got many or any to survive. If your duck is a muscovy, her eggs will need roughly 35 days to hatch anyway (chickens 21, turkeys and most ducks 28, muscovies 35). But the 35 for a muscovy is only a rough number. This year I had a muscovy sit through days 35 and 40 and 45 and figured the eggs were duds. Then on day 46 they hatched.
So candling will tell you a lot. There is a great series of pics here that will give you an idea of what to look for - the difference between a clear eggs and a developing, etc:
https://www.backyardchickens.com/t/...g-candling-pics-progression-though-incubation
Good luck and let us know how it goes...