There is an article in wikipedia - https://en.wikipedia.org/wiki/Space_elevator

But I have one question. Why elevator is planned on equator? What if it will be placed on the north pole?

There are 2 centrifugal forces - one is created by earth rotation, and another is by rotating earth around sol. Why it is not possible or efficient to use elevator based on the second force?

If you are inside the sphere of influence of Earth (See: https://en.wikipedia.org/wiki/Sphere_of_influence_(astrodynamics))  , You will be pulled towards the center of gravity. If you don't want  to come close to earth, you need to balance the pulling force in the  opposite direction. As you've mentioned above, You need to create  centrifugal force. Today, it's created by following (generally circular)  orbital path around the center of the  Earth. The orbital speeds depends  on how close you are to Earth. Closer you are, faster you need to go on  the orbit. Vice versa. Normally if you stop moving in the orbit, you  start moving towards Earth. This happens whether
 you are over equator or n/s pole. 

The  reason they propose for the elevator to start somewhere on equator,    has to do with geostationary orbits. Satellites on geostationary orbits,  need slower speeds to achieve orbital balance since they are farther  than the satellites at low-earth-orbit/LEO. In fact they have speeds  matching Earth's rotational velocity. This gives the illusion that they  are hovering always in the same spot but actually they are moving at  their orbit slow enough to match Earth's rotation.  

Since Space  Elevator's structure will expand from surface/some-point-in-atmosphere  all way to space, you need to put some balancing mass (space-platform?)  at the space-end to create sufficient centrifugal force.  If you put  balancing mass/space-platform at low-earth-orbit / LEO, It has to go  fast enough on orbit  to balance gravitational pull. It would be similar  to other satellites at LEO meaning It would go around the earth around  90 minutes or so (just like ISS). Imagine a giant , long elevator shaft  moving 7.8 - 8 m/s in the atmosphere . Never mind the air-resistance, It  would be impractical to have an elevator shaft moving fast like that. 

Instead  they came up with the idea of placing the balancing mass/space-platform  at around geostationary orbit in order to reduce relative motion  against the Earth to minimum. The relative motion is at the least when  elevator shaft starts on equator and go all the way up to balancing mass  at geostationary orbit. This way "Balancing mass-elevator shaft" system  moves very very slowly relative to Earth and you would have a stable  Space elevator. Of course current technology it is not sufficient to  create physical structure which can withstand even its own weight due  tensile stresses generated in such a massive structure.

An  alternate method proposes of putting the balancing mass at Medium Earth  Orbit / MEO and putting starting point of the elevator at the upper  atmosphere to reduce air drag and avoiding potential hazard due to the  moving elevator platform. But then there is the ever-present hazard of colliding with satellites at LEO and/or MEO since this system would go a lot faster then the equator-positioned model. There was a Space Elevator contest in 2010  with 2 main competition fields: Cable Tensile Strength, Powering the  elevator/carrier device. you should check it out : https://en.wikipedia.org/wiki/Elevator:2010 

For  your last question about using centrifugal force due to earth going  around Sun, I'm not sure on this one, I'm just gonna give you my guess.  As long as you are inside of earth's sphere of influence, you will be  affected by Earth's gravity for the most part; so centrifugal force  created on earth due to earth's orbit around the sun would not be  helpful ,in the slightest, to build a space elevator for earth. That  force only keeps Earth from falling to the Sun. You need to overcome  primarily the Earth's gravity.