Densities and Dimensions

[Infinite]

1. I was not able to find what the lesson to learn is in 6th dimension.

As the others replied, the lesson of sixth-density is balancement between love and light to reach the unity.

2. What also confuses me is how the mathematical dimensions in the universe (12 perhaps) fits into these levels of densities.

There is a subtle difference between density and dimension (although the terms are interchangeable). Density means vibratory frequence while dimension means a localization. But I will try explain.

You need imagine the concept of octaves. There are seven octaves of densities (first to seventh density). Within each octave or density there are seven sub-octaves. Within each sub-octave seven sub-sub-octave and so infinitely.

Our octave (third density) has 7 sub-densities divided in outer planes and inner plans or space/time and time/space. The space-time has 7 sub-frequencies which are the 7 levels of consciousness of the mind/body/spirit complexs. The time/space has 7 levels (that are which we calls "the others dimensions"). The inner planes have levels to each density level. I relate these levels with the densities, but when we talk about "dimension" we need to consider the space/time and time/space portions of the third-density:

third-dimension = physical plane
fourth-dimension = astral plane
fifth-dimension = mental or devachanic plane
sixth-dimension = causal or etheric* plane
seventh-dimension = buddhic plane

*Ra's terminology

But, these are only the "degrees" of vibration. The dimensions are infinity because there are infinite frequencies between each level and each sub-level...

About 12 dimensions read this channeling by Q'uo: http://www.llresearch.org/transcripts/is..._1218.aspx

3. When we talk about Heaven would that be same as 4th dimension?

The answer depends exclusively of the source from where the term came. But, generally the "heaven" is the higher astral plane (green-ray sub-density of Earth).

4. Are there humans (or more precise souls) living here on earth of higher dimensions than 3rd?

What did you mean by "living"? Incarnation? Yes, the Wanderers and the walk-ins.