Present perfect continuous

(1) She has been having a headache all day.

The sentence is wrong because the verb "have", when means " to suffer from an illness", is normally not used in the progressive tenses.

It's also wrong to say, "I am having a headache."

(2) She has been having lunch.

The sentence is correct because the verb "have", when means "to eat, drink or smoke something", can be used in the progressive tenses.

(3) I have been seeing an agricultural specialist.

The sentence is correct because the verb "see", when means "to have a meeting with somebody or to visit somebody", can be used in the progressive tenses.

The present perfect continuous shows that the action of "having a headache" began in the past, has extended up to the present and may continue in the future.
(1)If you show "all day LONG",you cannot show "continue in the future"any more.
If you want to indicate the possiblity of continuation in the future, then you can show on top of "all day LONG"=the mid-night time period onward to "6 or 7 am" time period !
If you suffer from headache which is a continuous pain in the head=please use continuous tense, which can be used to show" actions of headache" in future time, which shows that probability and intention.

(2)She has been having lunch shows that the action of having lunch began in the past, has extended up to the present and may continue in the future for some time,for some actions.=the possibility of continuation in the future.

(3)I have been seeing an agricultural specialist shows that the action of seeing an agricultural specialist began in the past, has extended up to the present and may continue in the future.It indicates the possibility of continuation in the future,which may concern doing business with the farming,the cultivation of soil,the workers etc.
An attempt to answer only.