KANJI GUIDE
The sky, and heaven with it. 天国 is paradise; 天気 is the weather.
The sky, and also empty. Buddhism uses the same character for emptiness — 空, śūnyatā.
A dream, both the sleeping kind and the wanting kind. 夢中 is being lost in something.
Long life, and the celebration of it. The character on wedding envelopes and New Year food.
The capital, and any big city. 東京都 is the Tokyo Metropolis; 都合 is how your circumstances stand.
Japan wrote London as 倫敦 long before katakana took over. That is where this character gets the ron sound.
弘める is to spread a teaching. The character in 弘法, the great teacher Kūkai.