Four separate functions, and one person or company can hold more than one of them.
The title insurance underwriter is the company that issues the policy and takes the risk on title defects. The title agent is the local business that searches the record, issues the commitment on the underwriter's paper, and gets paid a share of the premium. The settlement or escrow agent is whoever holds the money, prepares the settlement statement, disburses, and gets documents recorded. That role is neutral between the parties. The attorney is a licensed lawyer giving legal advice to a client, drafting or reviewing documents, and in some places conducting the closing.
So a closing attorney can be all four in one office: she runs the closing, she's an agent for an underwriter, she holds the escrow, and she represents somebody. That's why the words blur together.
"Attorney state" is market shorthand, not a legal term. Loosely people mean a state where an attorney customarily handles closings or where some part of the closing, examining title or preparing documents, has been held to be the practice of law. The strict answer depends on your state's statutes, court decisions and bar opinions, and those change, so ask a local attorney or your state bar rather than a forum. Recording practice, who may prepare a deed and what a settlement agent may do all vary by state.
On your last question: the escrow or settlement agent does not represent you, even when they're friendly and answer all your calls. The deed preparer doesn't represent you either unless you've engaged them. If you want someone whose duty runs to you, you hire your own attorney with an engagement letter.