Is there any sources for the prices of food over time and public transport?

You can take a look at the Consumer Price Index (CPI) which measures a weighed basket of goods that a normal resident will consume over a year and how the price changes over time.

I think an index for just 'food' or 'public transport' is harder to find. 'food' is very subjective (raw/cooked?, local/other culture cuisine?, hawker centre/restaurant?) so I dont think there will be such data. As for 'public transport', you'll also need to account for different age groups/distance/time/mode of transport/transit, I think there's data out there, just need to consolidate.