going very fast and suddently stops (maybe it is not possible but that is not the point)
Well, "stops" isn't actually well defined, but if it is subject to a thrust "backwards" any unsecured contents will all bang up against the "forward" bulkheads.
So, the answer is to your first part is yes.
Now, if there is an atmosphere present that will also slosh forward, but since it is a gas this will have no appreciable effect unless you have a helium baloon along--that will float toward the back of the vessel because buoyancy goes against the local effective gravity--or things get up to enough speed to encounter significant air resistance.
So the answer to your second part is mostly yes, things will still move forward with some specific exceptions.