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.
[NB: the OP seems to have changed using Catholic (in the title, as in Rome) with catholic (in the question, as in orthodoxy). I am answering using catholic (as a noun) with no intended disrespect to Catholics]
The correct sentence of your two examples is
My parents have the same religion. My father, hence my mother, is catholic.
The underlying sentence (main clause) is
My father ... is catholic.
the subordinate clause is
hence my mother (is also)
therefore my mother (is also)
thus my mother (is also)
making the subject of the sentence singular: My father.
Your use of hence is to mean therefore, thus, or so to show causality
Hence is an conjunctive adverb and is usually used to connect the two clauses
My father is catholic hence my mother is also catholic
My father is catholic therefore my mother is also catholic
My father is catholic hence my mother converted
My father is catholic therefore my mother converted
are correct to support the fact both parents have the same religion.
My father and my mother are catholic
My parents are catholic hence my religion.
are also correct.
The sentence
My father is catholic hence my mother
could mean that because your father is catholic he married your mother (for whatever reason)
Best Answer
Here the subject of the sentence is her parents. Because her parents is plural the auxiliary verb DO must agree with the plural noun phrase, so we need do and not does. The auxiliary verb DO is the first verb in the sentence. This is the verb that moves in front of the subject. It has no meaning, it just helps to make the sentence a question.
The verb after auxiliary Do is ALWAYS an infinitive. It can never be "Xing", "Xs", "Xed" or "to X".:
eats?went?liking...to come.It should be:
We can only have one auxiliary verb DO in a sentence.
However, the second DO in the Original Poster's example is the main verb. It's the lexical verb DO. It isn't an auxiliary. Because it comes after the auxiliary DO, it must be in the infinitive. The verb after auxiliary DO is ALWAYS an infinitive. Therefore the sentence must be like this:
Hope this is helpful!