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If you want to redistribute and/or modify TeX Live, please see the copying conditions.
As a general statement, the TeX Live maintainers agree, within the shared purpose of working on TeX Live, with the general principles and philosophy of the free software movement.
Therefore, to the best of our knowledge, all the software in TeX Live meets the requirements of the Free Software Foundation's definition of free software, and the Debian Free Software Guidelines. In the rare cases of conflict, we generally follow the FSF. Furthermore, the material in TeX Live should not require nonfree software to be useful. (Our package contribution page lists some more technical details.)
In short, this means that all the material in TeX Live may be freely used, copied, modified, and/or redistributed, subject to (in many cases) the sources remaining freely available. (Note: this statement is not true of all the software on CTAN.)
Of course, you must not yourself claim copyright (especially with a proprietary license) on TeX Live just because you redistribute it. Again, see the copying conditions for more information.
TeX and the other principal software in TeX Live runs in a terminal or command line and does not need an Internet connection to run. It is not a web application or “cloud” software. The software does not collect any personal information.
Donald Knuth released his original TeX and Metafont software, and Computer Modern fonts, to the public domain: TeX copyright page, MF copyright page, CM copyright page, article by DEK.
For a few of Knuth's files (tex.web, mf.web, plain.tex, plain.mf, hyphen.tex), he states that modified versions should be renamed. The relationship between this and the public domain declaration is not precisely clear, since TeX and MF long predate such legal wrangling, but in any case it is a reasonable and useful condition, and easy to satisfy. We don't recommend propagating a similar condition to any new files.
To state explicitly what is implied by the above: Because TeX Live is free software, there is no warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.