Step 1: Check the transmission route first.
Typhoid spreads through the fecal oral route, meaning contaminated food and water carrying the bacteria from an infected person, which matches statement I exactly.
Step 2: Check the Gram staining property.
Salmonella typhi has a thin peptidoglycan layer with an outer membrane, the defining structure of a Gram negative cell wall, so it stains pink, not purple, under the Gram stain.
Step 3: Combine the two checks.
Statement I about transmission is accurate while statement II wrongly calls the bacterium Gram positive.
Final answer: Option 3, statement I correct, statement II incorrect.