Solid Geometry and Booze

Bengt is lying in his pool, thinking. The pool is 25 m long, 16 m wide and 2.5 m deep without Bengt.
"Suppose that my weight will remain constant until I die, and that I will live a hundred years." thinks Bengt. Considering his food habits, those are somewhat unrealistic assumptions, but he doesn't care.
"Also suppose that my birth weight was 3 kg, and my weight so far has increased linearly. 10% of my body weight is blood, and the same is true for all humans."
Here, Bengt's thoughts are interrupted by the sound of the doorbell. Bengt leaves the pool. The water level sinks 0.25 mm.
It's Bengt's old friend Sture who comes to visit.
"Hello Sture." says Bengt. "Come on in. Would you like a drink?"
"Yes please. Some ethanol would be nice."
Bengt pours a glass for each of them.
"What are you up to these days?" asks Bengt.
"Oh, nothing much. I've started studying calligraphy, to write more beautifully, and stenography, to write faster. I'm hoping they will negate each other, so I can get a degree without learning anything."
"Why not economics and moral philosophy?"
"I'm not lazy enough. So, how about you?"
"I'm waiting for my evil twin to come back to Earth. He was sent out into space when we were born. He says he's going to come back this Friday, when I turn 50, and celebrate that he's only turning 49."
"Oh, wow. I had no idea you were so incredibly old. So what is this spaceship he has?"
"Well, it has constant acceleration up to a point, then constant acceleration in the opposite direction to turn, and then in the first direction again to stop, so that it has velocity zero relative to me when it lands over there." says Bengt, pointing. "I, on the other hand, have basically not moved since he left."
"But don't you exercise?"
"Yes, but it's negligible."
"So what fuel does the spaceship use?"
"Ethanol, just like you."
"It's a very good fuel. Have I told you about when I climbed Mount Everest from sea level driven only by booze?"
"Yes, many times. But it can't have been so difficult, because you only weighed 50 kg back then."
Sture tells the story again, just because it's so good. Then he leaves, and Bengt gets ready to jump back into the pool.
"Imagine if this pool was filled with gold rather than water." he thinks. "Then it would weigh as much as my brother's space ship. But it would be difficult to dive." thinks Bengt, and dives.

1. How far away has the spaceship been, from Bengt's perspective?
   
   
2. The space ship needs to carry its own weight, Bengt's brother (who weighs as much as Bengt) and the fuel. It has 100% efficiency, and ejects the exhausts.
   If it is powered by combustion, how much fuel does it need?
   (Remember that it also needs oxygen. The oxygen for Bengt's brother is negligible.)
   
   
3. If instead it is powered by fusion of the hydrogen atoms in the ethanol, how much fuel does it need?
   
   
4. If Sture climbed to the top of Mount Everest from sea level, without wasting any energy on anything other than the vertical movement, what was his blood alcohol content when he set out? (Assume that the ethanol is added to the blood mass and the body mass.)
   
   
5. Bengt likes to stretch out in the pool. If he could stretch out really really much, so he covered most of the area of the pool, would the surface tension be enough to carry him?
   
   
6. If the speed of light in vacuum is 1, how many m^4 is Bengt's whole life?
   

The Hourglasses

Bengt is visiting his grandmother, who lives in a very small and very old-fashioned village far out in the countryside. The village is so old-fashioned that there are no mechanical or electric clocks, only hourglasses.
In every house is an hourglass. Every whole hour the sand runs out in all of them, and the villagers instantly turn them.
But Bengt's grandmother is very very old, and now she has forgot to turn it. Bengt has to fix this by going to one of the neighbours to look at their hourglass. The problem is that one can only read the time when the hourglass is being turned, and the hourglasses are mounted on walls so you can't carry them away.
Bengt can walk with perfectly constant speed, and it takes only a few minutes to get to the nearest neighbour. He doesn't know exactly how fast he walks or how far it is, but he does know that there is a well at exactly half the distance.

How should Bengt go about making granny's hourglass catch up with the rest of the village? (Shouting is not allowed.)

A Wonderful Dream

Bengt is asleep in his bed, dreaming. In the dream he is in free fall with no air friction. It is almost dark; the only things visible are Bengt's glow-in-the dark watch, which shows that he is not supposed to wake up for another six hours, and a brightly glowing point of reference far away.
"What a lovely dream!" thinks Bengt. "An endless, homogeneous gravity field. The perfect opportunity to perform a really incredible twist... jump, or something. By moving my arms, I can make myself spin around and around."
Suppose Bengt's body is a cylinder, with height 1.8 m, radius 0.25 m, and mass 90 kg. His shoulders are represented by massless spheres, with radius 0.05 m, attached to the body on opposite sides. His arms are also cylinders, with length 0.8 m, radius 0.05 m and mass 5 kg each. The base of the arm-cylinder intersects the shoulder-sphere, dividing it in half, and spins around it.
He lets his left arm point forward and his right arm straight out to the side, then he moves them 90 degrees to the left, and then he brings them down parallel to the body. This he can repeat once per second.

1. If Bengt's mass is constant, what angular speed can he reach before waking up? (Assume that he can take any angular speed without expanding or exploding. It is a dream, after all.)
   
   
2. If the gravity is the same as on Earth, how far will he fall?
   
   
3. If all the energy needed for the rotation is taken from fat in his body, how much lighter will he get? (Assume that the fat is homogeneously distributed in Bengt.)
   
   
4. If he finally lands in his bed without bouncing back up, what change in velocity will the Earth get?