Hi - here's some suggestions:

Visiting Times in Hospitals
From my experience as a doctor, I can safely say that there isn't a perfect way to set visiting times in hospitals. The length and frequency of visiting times are dependent on each hospital's organisation,  the criteria of each ward and also on the condition of individual patients.

It isn't true that private hospitals allow visitors to spend more time with patients.  I know there is a private clinic in my city where visitors are admitted for an hour three times a day but I also remember a private hospital (which provided services for the NHS) where patients were visited at almost any time except during the night.  There are obviously exceptions on some wards, such as surgery or ICU, where particular hygiene regulations limit visits and specific permission is required to enter a ward.

When it is necessary for a patient to be examined or to undergo treatment then visitors have to wait or, if needed, to leave the room.

I've assumed you were refering to individual patients' conditions, but maybe you meant the conditions (i.e. the environment) in the hospital?  Taking an exam or sitting an exam is what a person does at college/university;  being examined is what happens in hospital.

Visiting time in hospitals

From my experience as a doctor, I can safely say that there isn't a perfect way to set (up) hospital visiting times/hours. The length and the frequency of visiting times depend on the hospital organization, patient conditions, and the particularities of each ward.

It isn't always/necessarily true that private hospitals allow visitors to spend more time with patients. I know of a private clinic in my city where visitors are only admitted three times a day, one hour at a time, and I also remember a private hospital (which provided services for the NHS) where patients are visited almost any time during the day, excluding the night.

There are obviously exceptions in some wards, such as surgery or ICU, where particulary hygienic conditions require less visitation or specific permission is required to enter the ward.
If someone goes to the hospital for a visit but the patient is in the middle of* an exam or he's being given an injection, then he, and all visitors, will have to wait or, if needed, leave the room.