I know dona means also bad. So, is there a difference between dona and droch? Is one worse than the other? And my next question concerns the hyphen between droch and aimsir. Why isn't it aimsir droch? Are there any more relations for aimsir, for example 'sunny weather' or 'stormy weather'? I am really curious about the multiple ways how to make sentences and how to use Irish idioms.
"droch" is just a negative prefix, like "ill-" in English (though it's not a translation of that prefix - there are places where you use "ill-" in English that you don't use "droch-" in Irish, and vice versa).
"dona" is an adjective, usually used with "go" - "tá an aimsir go dona" - "the weather is bad" versus "bhí droch-aimsir againn" - "we had bad weather".
Other than the negative prefix "droch", other adjective attach to "aimsir" in the normal way - "aimsir ghréine" - "sunny weather", "aimsir stoirmiúil"/"aimsir gharbh" - "stormy weather"
drochaimsir is fine, indeed preferable. The convention of always following droch with a hyphen in compound words is an old one.
These days, you would only keep the hyphen if:
- the word following it in the compound began with "c", for example droch-chlú (bad reputation);
- the word following it was already a compound word, for example droch + bun + scoil = droch-bhunscoil (a bad primary school);
- the word following it began with a capital letter, for example droch-Bhéarla (bad English).
There is also a handful of compounds that still seem to retain the hyphen, at least sometimes.