The Ossie motor

[futuristic]

And I would go with the top design because airgap betwen coil and magnets can be less than in bottom design.

[solinear]

Because of how magnetic fields work, the bottom design will work better - magnetic fields want to 'line up' and in the top design, they are lined up the entire time, whereas in the bottom design, they are not in-line until you hit the center. I've tried both styles in other testing and noticed a significant difference.  It's also easier to secure them against getting too close and touching, resulting in additional resistance.

[futuristic]

Magnetic fields of magnet pairs in both configurations are lined up all the time, because both are on rotor.
And magnetic field of coil is pulling that field into alignment with coil in both cases.
But smaller the air gap, the greater the force of pull.

[gyulasun]

...
2- now what shows the negative purple curve which is not affected by the red pulse. 

The neg. purple curve is the negative half wave part of the induced voltage during one full turn of the rotor.  Here is a good Java animation for seeing a conventional generator principle, the same happens in your present setup too:
http://www.walter-fendt.de/ph14e/generator_e.htm
Note the voltage waveform has a zero crossing just like you have, this happens any time when your rotor magnets are just between two adjacent coils. 
And if you choose the 'With commutator' position in the Java applet, then you just connected your full wave diode bridge to the coil outputs, and you get the negative half waves already turned upside and embedded between the positive ones. This is what full wave rectification like.

But if i try to charge my supercap directly from the bridge the Rpm first fall down and than as the cap charges they go up again.  Same thing with the current which first goes up and than down.

This is natural and shows Lenz law: the capacitor draws current while charging up, and current is taken from the induced voltage and this process exponentially goes on as the cap charges up: first the capacitor is empty, hence the charging current (which is the load current for the coils' induced voltage) is at its maximum, then current reduces as the stored voltage across the capacitor increases. Had you had a resistor load say a 10 Ohm) across the bridge output, your rpm would have reduced to a steady lower value and would have remained there.

Now the question     is my motor using the juice of the battery and go down and down 

I am afraid yes but I have not built such setup and cannot confirm this, please read and study Ossie's letter, it says the voltage in the battery can be kept at the same level IF you make the switches ON and OFF times correctly,  the letter is quoted on Naudin site,

http://jnaudin.free.fr/ossiemotor/indexen.htm#comments

and in counterpart the supercap pumps the energy of this negative Ac curve wich stay undisturbed by the pulse as is positive sister ?

No I do not think the voltage in the cap has "pumping connection" to the negative AC curve you refer to in your scope shot as you meant. In fact, that negative waveform is also used for charging the cap just like the positive waveform, the diode bridge changes the negative half to be also a positive one-- the bridge does its job, a full wave rectifier.

How can we put the supercap backstored energy in the battery   ?  Any idea ?   

Normally by using a dedicated DC/DC converter but it can only be 95-96% efficient in selected cases so you would have to have at least a COP of 1.04 - 1.05 coming from your motor setup to compensate for the converter 'underuntity' , to get a real selfrunner.  Others opinion are welcome here!
(On a real selfrunner I mean a device that has a COP>1 and part of its output energy can be used for solving its own energy supply.)

3- As the motor is an attraction motor, we agree that the impulse current  is independant of the magnet strength .correct?

If yes the bigger the magnet , the stronger the torque for the same impulse current? correct ? 

Yes for both, though it could be a repel motor too. 
I would vote for making such a motor with as many small coils in series and very strong magnets as possible to place on a rotor of a chosen size. Many magnets mean much more flux interacting, giving more torque.

So would it be a good idea to place a second magnet on the other side of the coil   so double torque for the same current ? correct? 

Frenky answered this and I agree with him, though I have not tried this on an air core coil. It surely works on an ferromagnetic cored coil. If it cannot be made to work, then the lack of a ferromagnetic core is the answer.

4- where and what is the best position of the magnet to the coil.  Must the magnet be round to fit the round aire core ?  Can it be a rectangular magnet with the aircore width but longer, covering the whole height of the coil ?   any idea ?   

Ossie explained where it is the best, read his letter referred to above
and see this scope shot

http://jnaudin.free.fr/ossiemotor/images/ossie2.jpg 

This means that it is better to use two switches, not only one. With the first switch you can choose the precise ON and with the second one the OFF time, Ossie says he positions the first reed horizontally and the second one vertically, you may wish to copy this with your second Hall sensor and circuit?  Or your using only one switch, positioning it also radially (not only sideways) from the rotor magnets, this may not give an optimum switch on-off timing, it sounds better using two independent things for fulfilling two independent tasks.

rgds, Gyula

[solinear]

Magnetic fields of magnet pairs in both configurations are lined up all the time, because both are on rotor.
And magnetic field of coil is pulling that field into alignment with coil in both cases.
But smaller the air gap, the greater the force of pull.

So the coil isn't there to be used as an electromagnet (attraction/repulsion)?  If not, then I don't think it's going to make a big difference between 1 magnet and 2 magnets.  You'll get more voltage from the higher flux density on the coil, but you're also going to get more drag on the system, from the increased wattage pulled from the coils.