1) The answer is both yes and no. Any particular digital circuit can be implemented, but not universal Turing machine, simply because there is no way to deal with arrays.
Yes, this is more like a thought experiment and it will require lots of efforts and money to realize it smoothly in a wet lab.
However, it is far more realizable than some other DNA implementations described in papers.
The idea to publish DNA code on GitHub with CI, tests, linters, badges etc. is obviously a form of joke, but the project itself was done like a serious applied maths research.
Yes, I've made CRN++ version as well (in this pull request: https://github.com/marko-vasic/crnPlusPlus/pull/1), but it required much more reactions and was less stable. So I decided to make it from scratch by using different approach.
There is mind-blowing paper, that gives exhaustive anwser to this question: https://hal.inria.fr/hal-01519828/document
This paper is about chemical reaction networks, but in 2010 it was shown, that any chemical reaction network is realizable in DNA: https://www.pnas.org/content/pnas/107/12/5393.full.pdf
2) Yes, it was figured out in 2006, how to do logic gates in DNA: https://science.sciencemag.org/content/314/5805/1585