Step 1: A young child with acute fever, tachypnoea, chest pain and a Gram-positive culture is the textbook presentation of community-acquired pneumococcal pneumonia.
Step 2: The slide shows paired, flame or lancet shaped Gram-positive cocci, characteristic of $Streptococcus\ pneumoniae$. On blood agar it is alpha-hemolytic, giving green partial haemolysis from $H_2O_2$ release.
Step 3: That same hydrogen peroxide injures host DNA and alveolar cells, driving the lung infection, and if it reaches the meninges it causes pneumococcal meningitis.
Step 4: Staphylococci form grape-like clusters, Propionibacterium is an anaerobic skin flora, and Mycobacterium stains acid-fast, so all are excluded.
\[\boxed{\text{Streptococcus pneumoniae}}\]