Where is the North of the Universe Does it exist North of the Universe? (Which is probably used for determining coordinates of far galaxies.)
If so, then where it is?
On what is it aligned? (Is it orientated on Earth, Sun, Milky Way, Local group or on something more bigger?)
Sort of... There is a system called the International Celestial Reference System (ICRS) which has center at the Solar System Barycenter (normally inside the Sun but not the same as the Sun's center) and which has the x and y axis in the plane of the Earth's equator and the z-axis ("North" if you will) pointing towards the Celestial Pole. The x-axis points towards the equinox where the plane of the Earth's orbit and the plane of the Solar system (the ecliptic) cross (on average; this gets complicated quickly as everything related to the Earth is wobbling about on different timescales).

Note although this reference system is close to the older mean equator and equinox J2000 or FK5 system it's not actually the same as it is now defined by a set of several hundred very distant extragalactic radio sources which are called the International Celestial Reference Frame (ICRF) and which we assume don't move on the sky. The latest version of this frame is called ICRF3 and was formally adopted at the IAU General Assembly last year in Vienna. More details on how the reference systems and frames work at the USNO page on the ICRS