Self propelling vacuum container in water If I understand correctly: a pressurized container can propel itself if you would take off the "lit" because there is now an open end that can no longer apply a normal force for the pushing gas, resulting in a net force at the other end of the container.
I would say the concept above applies if the container would be in space as well as if it would be in a medium such as water.
Now my question is: if we would now take a vacuum container underwater (I assume a vacuum container in space would just be called an empty container) and we would remove the lit, would it also be propelled (in the direction of the lit now of course)? 
Intuitively, one part of me says yes, as long as the difference pressure with respect to the water is the same the resulting force should be of equal magnitude in the opposite direction. 
However an other part of me says no, a low pressure inside the container would just decrease the time it takes for the container to fill up with water and besides the water rushing in would push the closed end of the container, resulting in no net displacement.
This little thought-experiment has been bugging me for the past couple of days so any input would highly appreciated! 
 A: It would move in opposite direction. This is because the pressure on the outside of the can and the force exerted on the can by the pressure is greater than the force exerted on the inside of the can because there is lower pressure. The net force is the opposite direction of the pressurized can, so it moves in the opposite direction.
A: I think you mean "lid", not "lit".
You're talking about a kind of rocket, and rockets work by conservation of momentum. It starts off quietly, with no momentum. If some mass flows out of the rocket, the remaining mass of the rest of the rocket goes the other way, so the momentum of the all the stuff remains zero.
Now, what if instead some mass flows into the rocket. The rocket will of course move toward the direction from which the mass came, so the momentum remains zero.
(Then of course everything stops, unless something makes mass keep on flowing into the rocket.)
There's a very simple way to think about it - a person standing on a frictionless rail car, with some bricks.
Putting bricks off the back onto the ground makes the car move away from them, because the center of all the mass doesn't move.
Doing the reverse, pulling bricks back onto the car, makes the car move toward them, again because the center of mass doesn't move.
Another way to think of it is - just reverse the clock!
A: You should look up working of the so-called pop-pop boat, in which a boat is propelled by alternate pushing out and suction of water into tubes underneath the boat. Also look up the famous inverse sprinkler problem (also known as Feynman sprinkler). See this paper: An elementary treatment of the reverse sprinkler_Jenkins.
I have conducted the experiment myself, by reversing flow in a plastic sprinkler using air as medium (air is sucked in using a vacuum cleaner), and I have found that it does not rotate in suction mode (but does rotate in the normal blowing mode).
In your case of the evacuated bottle, when you open the lid, two forces come to act on it. One is the pressure difference from ambient fluid, because where there is no lid there is a low pressure zone, while on the opposite side of the bottle ambient fluid exerts higher pressure (from outside). Then there is flux of momentum due to inflowing mass, that adds momentum to the bottle in the opposite direction to which pressure difference is acting. Whether the two will balance or not is difficult to predict by analysis because the flow can be complicated. However the general consensus seems to be is that it doesn't move. But I recall having seen a video of just such an experiment on University of Maryland website (which has a list of questions and answers) where they found that sprinkler rotates in the same direction as it did in the case of normal operation (actually it was a long time ago, and I am not sure whether it was same or opposite direction, sorry!). So conduct an experiment yourself!
