Most of us quickly made casual friends as you described, but are yet to make many close friends. As for integrating into society, most of us found society quick to help and welcome us, but struggled to move on from "the foreigner that needs help and teaching" to "the person with ideas and opinions as valid as an equivalent Japanese person", this is irrespective of Japanese ability.
Perhaps that is why many people says it's difficult to integrate, what we immigrants want from integration and what Japanese society wants from integrated immigrants is fundamentaly different.