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- Over half of the domestic flights were delayed because of bad weather condition.
Is this correct to use "were" here?
What if "one half" is used instead of "over half"?
- One half of the domestic flights were/was delayed because of bad weather condition.
Which is correct for #2, "were" or "was"?
What if we remove the definite article "the"? Does it affect the use of plural/singular verb?
- Over half of domestic flights were delayed because of bad weather condition.
Half is half of one (or for that sake whatever number you have), so no need to include 'one' there. About singular/plural verb, you are talking about more than one flight, so it takes 'were'. Moreover, putting 'the' here ensures that you are specific about domestic flights that got delayed because of the weather condition.
'half of the' or 'half of' makes a separate (and also good) question though.
In all those cases you want "were" because the subject of the sentence is not "half" it's flights. Here "half" modifies "flights" by telling you the portion of them.
Flights were delayed.
Is the core of the sentence. You then add the portion and reason on top of that.
Consider:
Half of the apples were rotten.
Half of the apple was rotten.
There is a special exception for the quantity one though:
One of the apples was rotten.
The one actually makes the whole phrase singular despite "apples" being plural. Logically we must be talking about a single apple. But in:
One half of the apples were rotten.
"One" modifies "half", not "apples".
