I'll answer your questions from his book, A Memoir of Grace, by Chuck Smith (2009).
- Which Christian denomination(s) recognize his organization, and which ones do not? Why?
I don't know the answer to this question. Not sure what you mean by "recognize," for I would recognize any organization if it had regular meetings and members. Do you mean anything different from this?
- What was his leadership style like, and what made it distinctive?
The book did not address this, other than to say that he believed in not placing any programs or techniques above the sovereign work of God. He kept everything simple; just teach the whole Bible, book by book, chapter by chapter.
- Which Christian denomination(s) is/are in conflict with his theology, and which one(s) is/are most in harmony?
Any denomination that sets rigid plans and programs would be in conflict with his theology of the moving of the Spirit. He specifically talked about an earlier version of a Foursquare church that set church competing against church to do membership drives, and those who drove in the most members "won." Chuck rejected this program approach after a time of prayer where the Lord spoke to him that He Himself will "add to the church daily." He went on preaching as usual and got more members by simply preaching the word chapter by chapter. His superintendents invited him to come to the next convention and tell the others what techniques he used to such great success!
- How were his congregants' lives any different than other Protestants' lives?
Chuck found that by teaching through the whole Bible in depth, Genesis to Revelation, the people got more out of it. Expositional preaching, as opposed to topical preaching or gospel preaching. They were more grounded in their faith and were excited to tell others about Jesus and the Bible. Calvary Chapels sprung up all over the world without Chuck making 5-year church-planting plans or anything like that.
- Who was Chuck Smith, and what was his place in Christianity?
Chuck Smith will always be known as the person who started Calvary Chapel Costa Mesa and the person who helped the hippies' brand of Maranatha! rock/contemporary music spread everywhere.