"天“ means day or sky. "多美 (what wonderful)的一天 (a day)啊” means "what a wonderful day"; "多美的天啊“ means " the sky is so beautiful".

In Chinese, almost every character has multiple meanings depending on the situation where its used. 天 tiān could refer to sky, day, weather, natural and more if you look it up on dictionary. In this scenario (多美的天啊) the 美 (pretty) is related to the word 天, we usually refer 天 to sky because the adjective pretty is used to describe the object sky. I would say 多美的天空啊 will be more exact and complete. I will generally say this if I see something beautiful on the sky, like watching sunset during the evening.

多好的人啊！ 感叹句 exclamatory sentence 多……

It depends, It means lovely day. or beautiful sky.

other 天=sky or day