did she perform it live anywhere?
Yes, at Hearst Greek Theatre and  Austin City Limits Festival.
Yellow Flicker Beat
On 2 October 2014, Lorde performed "Yellow Flicker Beat" for the first time at Hearst Greek Theatre in Berkeley, California. Later that month, she sang the song at the Austin City Limits Festival. The overall performance was praised. It was also performed as part of Lorde's Melodrama World Tour (2017–2018) during the North American arena leg.
what is the song everybody wants to rule the world about It is a new wave and synth-pop song. who wrote the lyrics for this song? Roland Orzabal, Ian Stanley, and Chris Hughes. is this part of an album? Yes, "Songs from the Big Chair". does any other singer have their own version of this song? Yes, Lorde. when did she release her version? 2013 what other hit songs has she sang? "Yellow Flicker Beat" and "Melodrama". what kind of image does she have among the public? She described her public image as something that "naturally" came to her and was identical to her real life personality. Lorde identifies as a feminist. how well was her first song mentioned above received? It received mostly positive reviews from music critics.
wiki:4837780
Yellow Flicker Beat [SEP] Live performances
On 2 October 2014, Lorde performed "Yellow Flicker Beat" for the first time at Hearst Greek Theatre in Berkeley, California. Later that month, she sang the song at the Austin City Limits Festival. The overall performance was praised. It was also performed as part of Lorde's Melodrama World Tour (2017–2018) during the North American arena leg. Lorde performed the song at the 2014 American Music Awards on 23 November 2014. She began the performance by singing inside an "orange-lit box". Halfway through the song, the box was lifted, revealing Lorde wearing a white crop top and black pants outfit to the audience.