This is the Roman-era bema or speaker's platform. Or it might be. As with most sites things have been built on top of other things.
Paul was in Corinth ca. 49-51 AD. While there, as Acts records, he was brought before the proconsul Gallo, presumably at this bema, or perhaps in some other setting.
Cf. Acts 18:1-18 and 19:21 as well as 2nd Timothy 4:20 and the letters to Corinth, of course.
Paul's letters to Corinth date later, perhaps 57-60 AD.
Eating food consecrated to idols
Doesn't sound like an issue we care about. However, the general concept is still an issue. If someone else cares about something; but we don't - what is the impact of our doing that thing? Is it meaningless - since we don't believe in any consequences from it - or do we give it meaning in relation to the other people.
The second dynamic is what those who are "strong" owe to the "weak." The strong are those who understand that idols don't exist and aren't affected or disturbed by eating their meat. The weak, perhaps a bit more superstitious, are worried.
Should the strong moderate their behavior out of genuine concern for the weak? In other words, do rights need to yield to love.
The application to today is obvious enough.
Just how wild and crazy was Corinth? The famous quote about there being 1000 temple prostitutes is unlikely to be true. But the city was a seaport so lots of people were away from their social controls. But does this matter in understanding Paul - his community could be different than the larger city.
Freedom, and how much of it is good. (1Co 10:23 NRS) "All things are lawful," but not all things are beneficial. "All things are lawful," but not all things build up." So, making a fetish of freedom seems to be bad. Just because you have the right to do something, doesn't mean it would be good to do it.
Role of women. Much is made of Paul's alleged anti-women stance, and one can certainly wish he'd chosen to be more unambiguous. But there seems to be less here than meets the eye. He speaks of women prophets but then seems to say women should be quiet - so people widely think he contradicted himself, or even that the words were added by someone else. There is a simpler, and less nasty, interpretation. It is women in the rank and file of the congregation he wants not to disturb the worship - and not to disturb the men and women leading the worship. He has a series of examples, and they all point the same way: do things "decently and in order", don't disrupt the proper worship - but it's not aimed against women per say - as the letter is full of references to women in leadership positions.
Christians in relation to the Empire. A neglected subject. But Paul is writing to people who've put themselves outside the normal social life of the empire and put them into suspicion by the state.