In which country was the Deseret alphabet used?
This is about a writing system rather than a language. The language for which Deseret was used was English, and the country was the United States.
The Deseret alphabet was developed from 1847 to 1854 by George D. Watt, under the direction of the Board of Regents of the University of Deseret. The Board was headed by Brigham Young, second president of The Church of Jesus Christ of Latter-day Saints.
Young claimed that Deseret was to replace the traditional Latin alphabet with a more phonetically accurate alphabet for the English language. This would offer immigrants an opportunity to learn to read and write English, the orthography of which is often less phonetically consistent than those of many other languages. Deseret was one of several proposals developed in the 19th and 20th centuries.
As an example of the problem that the Deseret alphabet was designed to address take the word "Information": some find it odd that the final syllable "tion" is pronounced like "shun".
The picture in the question illustrates Deseret. The five lines represent the sentence "Information wants to be free" in five different computer fonts. You can spot that, in the second word "wants", the "W" is much the same in Deseret, the "N" that appears twice in "Information" looks like a backward "N" in Deseret and so on.
Deseret was never widely popular, and usage had gone into decline by the end of the 1870s. But you can still get the fonts on your own computer, if you are interested.