I'll answer the easy part of the question first: no, the U.S. has not suspended its diplomatic relations. It has simply closed its embassy at this time.
It has been reported in the media that the reasons for closing the embassy were related to the security situation in Damascus, which was particular to the U.S. embassy and to certain threats they felt they were exposed to; the media also reported that the Syrian regime could not give assurances that it would be able to provide sufficient security for the embassy, so the closure of the American embassy was based on a rationale that applies to the particular U.S. situation in Damascus.