1. What should be done if acute symptoms such as headaches, irritation of the respiratory tract and/or eyes are observed mainly when one is in some premises?

2. What should be done if a person suffers from chronic or recurring respiratory diseases that do not seem related to a pathogenic cause (such as viruses or some lung bacteria)?

When symptoms are observed the first thing that must be done is to talk to a doctor. The family doctor can consider all facts about you and make the proper diagnosis.

6.2. Pathologies rencontrées au cours des audits Environnment-Santé_FR_ISP

If the conclusion is that it is an allergic or toxic phenomenon that is undoubtedly related to environmental factors of your home, he, along with you, will identify the potential sources or may get an analysis of your indoor environment conducted by relevant local departments: 

Wallonia region: Ambulances vertes (Green ambulances)
Brussels Capital Region: Cellule Régionale d'Intervention en Pollution Intérieure (CRIPI)
Flemish Region: Medische milieukunde in Vlaanderen (MMK)

Other interesting sites:

Indoor Air Quality - European Website
Indoor Air Pollution Guide