Can Traffic Server run in forward proxy and reverse proxy modes at the same time?
Yes. When you enable reverse proxy mode, Traffic Server remaps incoming requests according to the map rules in the remap.config file. All other requests that do not match a map rule are simply served in forward proxy mode. If you want to run in reverse proxy only mode (wherein Traffic Server does not serve requests that fail to match a map rule), then you must set the configuration variable proxy.config.url_remap.remap_required to 1 in the records.config file.