Question about the direction of a frictional force 
I guess that this can be applied to any similar situation, but just to be on the safe side I will ask for this concrete situation. So we have a screw press, by turning the screw we move the block no 2 to the right, and therefore the block no 3 is going upwards. I need to find the axial force in the screw. To do this I need to make (among other things) a free body diagram of the block no 3.
This is all just so you get the context of my problem, which is this: Why is the friction on the block no 3 going the the right? Like in the picture below

It implies (does it?) that the block wants to move to the left, which just... I don't see why. This also raises another question - for sum of the horizontal forces to be zero, there must a force Fn1 (painted in blue) - now where does this force come from? Looks like, thin air.
I'm hoping someone can give me an intuitive way of understanding this, as well as a technically correct one
 A: Here's a very simple trick. Let me first introduce it in the context of a door:

A door is hanging from two hinges as per usual. Is the bottom hinge pulling in on the door, or pushing out on it?

The trick is, imagine that we instantly take away the hinge. What happens? The bottom part of the door crashes into the frame. So what does that tell us? That the hinge was pushing out, not pulling in.
Similarly, imagine that the box or tube or whatever it is holding this block in place, did not exist.  What direction does the friction force take the block? Rightwards. So it's a rightwards force.

Skipping trickery, friction forces usually oppose velocity: so if I am out sledding on a hill which faces North, so that I am travelling Northward, there is a Southward friction force on me. 
But you have to be careful on what velocity you mean; equivalently, you can transform to my reference frame, in which case you'll see the ground moving Southwards out from under me. The force on me doesn't point North to oppose this velocity! In fact the principle is still the same, I am exerting a friction force on the snow which is pointed Northward (I might even drag some snow with me!), and therefore the snow (due to Newton's third law!) has an equal and opposite reaction force on me.
A helpful hint that you've got it right/wrong is to remember that the friction wants to "stick" both objects together, so see if the tendency of the force is to bring the velocities closer together or further apart. 
A: Friction opposes relative tangential motion (or the tendency towards relative tangential motion) between the surfaces in contact. 
Friction from block 2 is pushing on block 3 towards the right. As CR Drost puts it, friction tries to stick the blocks together. (I qualified this by pointing out that friction only acts along the common surface, it does not oppose the surfaces being pulled apart .)
Block 3 tries to stay where it is. So This is because, relative to block 2, block 3 is trying to move left, so the friction force on block 3 acts in the opposite direction - to the right.
Why is block 3 trying to move to the left (relative to block 2)? Because it is trying to stay where it is. The vertical cylinder housing of the press prevents block 3 from moving to the right along with block 2. This cylinder wall provides the force $F_{N1}$ which acts on block 3 to the left. If the cylinder wall were not there then block 3 would still try to remain in its current resting place, because of its inertia.
