1945
July 16, 1945 was the first nuclear bomb test by the United States.
US
US, July 16, 1945, Trinity site, NM, in what is now White Sands Missile Range.
In remote isolated places. Most testing (except for a few countries) is now done underground, to prevent fallout. The US has ceased all physical testing and uses only computer simulated tests.
US performed nuclear test at Nevada Test Site
1949, it was a clone of the US Fatman design based on stolen plans.
I believe the first underground nuclear test explosion was done by the US at the Nevada Test Site. However it was not intended to contain the blast or radiation. It was an effects shot to evaluate cratering, the bomb was only 3 feet underground. It was part of the 1955 Teapot series.
US, July 16, 1945, Trinity site, NM, in what is now White Sands Missile Range
Yes, an underground nuclear bomb test has the potential to create seismic waves that can be detected and recorded as an earthquake. The magnitude of the seismic event would depend on the yield of the nuclear explosion and the geology of the surrounding area.
US
To end WWII.