Thumb rule and right hand rule are for conventional current or electron flow ( for finding N, S in wire and winding)?
In a real experiment for finding true N , S what should I do?
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When considering Lorentz force, right hand rule is for negative charges, so electrons. Left hand rule is for conventional current(notice that current is always just pointing in the opposite direction to velocity in the right hand side, which is like the derivation of conventional current that positive charges going one way is the same as negative charges going the other). The field finger(first finger) points in the direction of the field lines, which is the direction a north pole would move if it were in that position. Remember "thumb rule" instead like a corkscrew or door key. The way you turn the key into the door(direction of current) is the circular locus the magnetic field would take. Since north poles repel each other, the field finger points towards the south pole. Then naturally from dipole law, opposite direction must lead to a north pole.
In a winding, use a right hand grip rule (thumb stuck out). Conventional current flows in the direction of the fingers, then magnetic field within the winding is in the direction of the thumb.
The rule also works for magnetic field around a current. Thumb in the direction of current, fingers curl in the direction the field goes.
To test whether a pole is north or south, set up the coil and battery and see what happens. Or use the Earth, always remembering that because the North (short for north-seeking) pole of a magnet points roughly geographically north, the Earth's North Magnetic Pole is, in magnetic terms, a south pole.
With the right hand thumb in the direction of positive current, the fingers wrap around in the direction of the magnetic field. The field comes out of the north (seeking) pole of a magnet or current carrying solenoid. (When working with a vector (cross) product, hold your right hand so that you can curl your fingers from the first named vector toward the second. The thumb gives the direction of the product.)