Right Hand Rule Magnetic Force

[Redfire66]

I'm just really confused with this right hand rule even though it seems like it's supposed to be pretty simple and obvious. I know the rules, however it doesn't really work for me. Maybe I'm doing something wrong. I have three examples I'd like to cover which are related to each other, I hope someone would be willing to help.
So let's say I have the diagram attached. And so there is a wire that is coiled to make a square on the left side and a wire by itself. These diagrams are separate of each other.
The line (image on the right):
I was told to coil my hand around the wire, thus the magnetic field goes (According to my fingers) out of the page above it, and into the page below it. Then the force would be upwards above it, and downwards below it (so pretty much the field is circular I assumed). Okay this makes sense, I'd rather draw a circle since I get mixed up.
I'm having trouble connecting this with the square coil.
Square Coil:
The second method I was taught is to point my thumb towards the current, and curl my fingers to get the field. So I did that.
However... I was told that the force points away from the center by my professor. He tried explaining it to me after the lecture about the right hand rule however it still didn't make sense, I was wondering if anyone could help explain this. It seems weird to me, I see the magnetic field as circular more than a straight line so I assumed there was a force away (let's say to the right for the right side of the square above the wire) and towards the center (below). Is this because the forces acting towards the center counteract each other due to symmetry and leaves the remaining forces to act away from the wires?
Lastly the Picture 3:
Going back to that square coil (it's supposed to be 3D this time) which seems to be giving me a headache, if we were to rotate it sidewards and lift it up which is the bottom image (hence there is a gravitational force on each wire); This gravitational force acts on the wire and pulls it down. If it were inside a magnetic field pushing upwards and I were to hold one side to keep it at some angle, how would I know what the direction of the field of the current is? Would it be at the same angle parallel to the wire?
If I'm not explaining clearly then I can re-explain. Thanks

Edit: The rules which are in my textbook were
1) Point fingers in direction of current => Bend fingers toward magnetic field => Thumb = force
2) Point thumb towards direction of current => Curl fingers around it which gives magnetic field (Not really sure about this one I guess it doesn't give direction of force which is fine since I can use the other one)
3) Point thumb towards current, and fingers to magnetic field; Palm gives the force direction

 

[Simon Bridge]

Line image: use "right hand screw rule".
i.e. You point your thumb along the direction of the current and your fingers will curl in the direction of the field.
As you noticed, the field is circular (cylindrical) about the wire.

It is the same for the square loop on the left top. Here you have four straight sections and the magnetic field from each section adds up.
So you have to use the above trick four times.

When you did this - what did you get?


When a wire with a current in it is in a magnetic field, it will experience a force given by the "right-hand slap rule".
You'll need to look it up.

 

[Redfire66]

Oh okay, I understand. I misunderstood the whole thing. I assumed that there was a force with no magnetic field which seemed kind of weird to me. Thanks for clarifying.

 

[BvU]

Maybe you can benefit from browsing an older thread here
(not sure; your post was a bit long and perhaps your bottleneck differs)