Does oData using lightning connect syncs automatically? If yes then what is the frequency? If no then how the sync happens?
It does not sync automatically. Salesforce Connect only syncs when you ask it to.
Salesforce Connect will re-read the $metadata document over time so you will see Salesforce send GET requests against it periodically (a data type on the Salesforce side could map to a column of many different data types on the OData side, so this confers some flexibility to adapt to minor changes on the remote end). But Salesforce Connect will NEVER alter the External Object metadata or its custom fields automatically.