あなたを商標登録しました means "I've registered you as my trademark", referring to the recent event of a vtuber registering a famous type of Touhou derivative works as a trademark.
ドンブラザーズ (Avataro Sentai Donbrothers) is a tokusatsu TV show made by TV Ashahi, inspired by the Japanese tale Momotaro.
ウマ娘キャラ診断 means Uma Musume character diagnosis, an online test that tells you which Uma Musume/horse you are.
上島竜兵さん is Mr Ueshima Ryuhei, a Japanese comedian and actor, who was found dead on May 11.
メイドの日 means Maid's Day, from the wordplay of the Japanese pronunciation of the date May 10.