Generally it was recognized as a power after the Russo-Japanese war, it proved it could compete at the same level as European states (albeit Russia). That said however, it was never fully recognized as a great power. WW2 forced everyone to recognize Japan was a major power, which led to its defeat.
Symbolically, the below events could be put into consideration.
1894 : Britain abolished the extraterritorial right in Japan
1895 : Japan defeated Qing Dynasty of China and concluded the Treaty of Shimonoseki
1899 : All great powers abolished the extraterritorial right in Japan
1902 : Anglo-Japanese Alliance
1905 : Japan defeated Russia and concluded the Treaty of Portsmouth
After 1905, Japan was undisputedly a "first-rank great power" recognized by other countries.
No, it's not. Throughout the 19th century we have examples of Haitians (against the French, Spanish and British), Mexicans (against the Spanish and French), Ethiopians (against Italians) and even Indians (the Marathas against the British, even if they got colonised in the end) defeating Western powers. The Russo-Japanese War and any of its battles were not the "first time" a non-Western, non-European power defeated a Western power.
Great Power is just a title and a Euro-centric one at that, Japan already had the ability to overwhelm powers such as France, Austria, Italy, and Germany in Asia since the 1890s, if not earlier. One could argue Japan was already a great power by 1899, when it was able to nullify extraterritoriality on its own soil by western powers. Statistically, the Japanese navy was probably already a match to the Austrian navy by 1900, although its army was somewhat smaller. The Japanese Empire's population was roughly equal to the Austro Hungarian Empire at around 47 million and greater than Italy's. However, Austria and Italy were a lot more industrialized than Japan and had higher GDP total even down to WW1. Italy for example, still produced over twice as much iron as Japan did in 1900, this gap would only increase to 4-5 times by the 1910s. So if Japan was only considered a "great power" after 1905, then that's only a prestige issue since statistically, it should already be one in 1900.