When you deal with vacuums like this, you may be dealing with rarefied gasses. Normally with gasses we assume there are so many random collisions that we can treat velocities as random distributions. This is true in most environments. However, as you decrease the pressure, they start to change. We start having to pay more attention to the specific collisions and we start having to treat the gasses as ping pong balls. When you get to this state, you only get to assume random distributions if you can demonstrate that it's a reasonable assumption.
Thus, the answers to these questions depend a lot on the size of the apparatus and the pressures. The "mean free path length" is a measure of how far a gas molecule goes before colliding. The longer it is, the longer it takes for the gas to reach a nice easy statistical ensemble where you can treat things as random.
- Now when we open valve A will the gas move in one direcion towards valve B ?
The instant you open the valve, the system is no longer in equilibrium. All molecules will generally start moving counterclockwise. At some point, the path lengths may get long enough that we can no longer treat it as a normal gas, but instead must treat it as a rarefied gas, which will matter for your next question.
- If valve B is opened when the gas is about to reach it, will the gas be moving towards valve B when it used to be closed at a constant speed?
At this point, you should treat the air like a bunch of ping pong balls. They have no idea that valve B exists because there hasn't been a bunch of random collisions ahead of the gas to pass that information clockwise. As such, you should expect it to work just like a bunch of ping pong balls. They'll keep moving, unaffected by value B, because they're just particles.
- Will there be any decrease in its speed if there are some obstacles through which it can pass?
Use the ping pong model again. If you put a bunch of obstacles in the way of ping pong balls, would they slow down? The answer, of course, is yes.
Interestingly, we also see putting obstacles in front of normal gases can slow them down too. The effect is very noticeable at high flow speeds. We call it "drag."