Is there always a stall if you exceed a specific angle of attack?
Yes, stall depends only on angle of attack. However
Does this mean, that, at whatever speed you are flying (i.e. 500 knots), you would stall if you go on a climb angle of more than 16°?
No. Climb angle and angle of attack are completely different things.
pitch, angle of climb and angle of attack http://www.av8n.com/how/img48/incidence.png
This image from How It Flies shows the four different angles involved. Pitch is the angle between aircraft floor and horizontal, wing incidence is angle between aircraft floor and wing¹, angle of climb is angle between flight path and horizontal and finally angle of attack is angle between flight path and wing.
The image shows that angle of attack + angle of climb = pitch + wing incidence.
Up to stall, lift depends approximately linearly on angle of attack and square of speed (and on air density). In straight flight the forces on the aircraft need to be balanced, so angle of attack will be such that they are. If you increase pitch, the angle of attack will increase, which will cause unbalanced force, which will cause upward acceleration and that will increase the climb angle at the expense of the angle of attack again.
So if you go on a climb more than 16°, the angle of attack will not significantly differ from what it is when you fly level at the same speed.
I am just wondering, since, if you fly in the microsoft flight simulator with a big jet, you can have an angle of attack of 30° and more, and not stall until you get to the stall speed.
No, you can't. You, however, can climb at 30° or more, for a while before you run out of speed. Which at low altitude is actually quite long; the jet engines are designed to have enough power at high altitudes where air is much thinner and to allow taking off when one engine fails late in the take-off roll. Therefore low with all engines operating at full power you have quite a bit of extra thrust available.
Also note, that stall does not mean loss of all lift. You only loose part of it. A significant part, but not all. Stalled aircraft is still controllable (though ailerons effect is reversed) and some aircraft (though this would be fighters, not airliners like 747) may even have enough lift and thrust to maintain altitude when stalled.
¹ Specifically, the zero-lift line of the wing. This coincides with the chord of symmetric wings, but cambered wings have it tilted up.