I mean is there any rule to avoid spelling mistakes in these cases?
Why we write homemade but we cannot write readymade, and we write ready-made instead?
Also why shut down and hand over are verbs while shutdown and handover are nouns?
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No rule. Spellings do change over time and compound words that used to be written with a space tend to get joined with a hyphen and ultimately merged into one.
For example, in the 1500s you would have a tooth brush. In the 1600s it was written "tooth-brush" and now it has become "toothbrush"
On the other hand "Rain forest" only entered English in about 1900 Until 2000 it was usually two words, now it is increasingly spelled as one word "Rainforest". This change in spelling is happening now.
But there is no way of knowing. Fortunately, spelling is very forgiving about putting a hyphen in. Most people would happily accept "fire fighter", "fire-fighter" or "firefighter" and would understand "rain-forest" or "tooth-brush" (although that would be odd). There are very few examples where the meaning can be changed by a space or a hyphen, and some spellcheckers will spot and correct incorrectly split compounds.