When the Messiah comes, will it mean that society will not function as it does today? Will there be attributes of today’s society that will stay the same even after the arrival of the Messiah such as economics?

According to Maimonides, society will function essentially as it does today, but the Jews will not be subjugated by any other nation. The Ramban opines that there will actually be a change in human nature, and that would impact on the matters you mention. In any case, we have no clear tradition as to what exactly life will be like in messianic times.