天气非常地热 this is wrong, u should use 得. like this: 天气非常得热 adv + 得 + adj / adv / v 非常得热 = 非常热, which means u can omit 得 here 地(di)热 has two meanings: 1) a kind of heating radiator for apartment. for some apartment, we put the heating radiator under the floor, so it is called 地(di)热 2) 地(di)热 or 地(di)热能. this is a physics-word. it represents a kind of underground energy. we can find it from some natural phenomenon, such as volcano, hot spring etc.

“地热” is not one word. "地”is a particle word here without any special meaning, you can omit it. So these two sentence have exactly the same meaning.

There is no differences.天气非常地热.和 天气非常热.意思是一样的."地" has no real meaning. "地热"is not a word.

“的、地、得”是连接句子的。是不是更热要看口语的语气，从短句的文字上看没有区别。用“地”更繁琐，直接写“天气非常热”比较好。

if you see "地热" as one word -- it's a noun but in your sentence it's not one word it's “adv 地 adj” construction 天气 非常 地 热。