If i am touching various objects in a public space in a large city with my hands and i do not wash my hands before i use my fingers to eat something, what are all the diseases i can catch and what how likely am i to catch them?

Colds, influenza: Contrary to popular belief and many persons' fears, few infections are caught by contact from the environment. The most common by far are colds and influenza (during flu season). Use common sense hygiene, e.g. frequent hand washing and/or an alcohol gel like Purel. Otherwise no worries.

Very few: Survival depends on the intrinsic resistance of our bodies to environmental hazards Folks touch things all the time in public spaces and if you notice, very few people eating in restaurants wash their hands prior to eating. And most do not get any illnesses and you will no doubt be fine as well. The most likely thing you might get is the flu from atmospheric carried viral particles.