日本語 Pronounced- Nihongo (Nee-hon-go)
It can be written: こめ in hiragana. And: 米 in kanji.
Nihongo. See here for a graphical representation: http://www.therealjapan.co.uk/images/nihongo.jpg
はいく The first character is "ha", the second character is "i", and the third character is "ku". This is written in hiragana. There may be a different way to write it in kanji.
世界の芸術 /se Kai no gei ju tsu/ means 'art of the world, world's art' in Japanese.
The Japanese Art Form of Lacquer
How to Choose a Japanese Calligraphy Character
Japanese 3D Nail Art Harajuku-Style
The Art of the Japanese Death Poem: Basho's Last Stanza