You are not required to set severity level for sending syslog messages to a server. There are a number of options you can use to fine tune how you send syslog messages to the server, including severity level. But setting the level is not a requirement.
Like I said in a previous post, there are other options that you might use to fine tune your logging. But the only required steps to get syslog sent from the ASA to a server are to enable logging and to configure the host to which the syslog will be sent.
Yes your server must have a syslog app running on it if it is to receive and process the syslog messages.