I read many years ago about the meaning of TeX, coming from Greek letters, etc... Also I found many posts here related to the right way to write TeX, LaTeX and so on when it is not possible to use the macro \LaTeX.
But my question is: why are the letters a and e moved on the logo?
As you mentioned: 'TeX' comes from Greek τέχνη and the capital τ (tau), ε (epsilon) and χ (chi) are identical to a Latin capitals T, E and X respectively).
Artistically, writing the epsilon as a 'lowered' capital makes sense not only because the capitals are identical. It also shows (a tiny bit of) the capability of TeX: It shows that TeX can do proper kerning, with subscripts as well.
Maybe it's best to let Donald Knuth explain:
[...] it’s important to notice another thing about TeX’s name: The ‘E’ is out of kilter. This displaced ‘E’ is a reminder that TeX is about typesetting, and it distinguishes TeX from other system names. In fact, TEX (pronounced tecks) is the admirable Text EXecutive processor developed by Honeywell Information Systems. Since these two system names are pronounced quite differently, they should also be spelled differently. The correct way to refer to TeX in a computer file, or when using some other medium that doesn’t allow lowering of the ‘E’, is to type ‘
TeX’. Then there will be no confusion with similar names, and people will be primed to pronounce everything properly.
(Source: The TeXbook)
As for the La bit: Placing the 'A' underneath the 'L' would look a bit strange:
TeXbook: 'The E is out of kilter ... [which is a] reminder that TeX is about typesetting, and it distinguishes TeX from other system names'