I find the logs of the full node kind of confusing.
How to know when my full node is syncing or if it is fully synced?
When retrieving node info from your node, you will see
latestMilestone as well as
latestSolidSubtangleMilestone (this will also appear in the status bar of the wallet if you use it to connect to your node).
If the values are the same as the majority of nodes listed on https://iotanode.host/ (or another site that fetches and aggregates milestones of public wallet nodes), your node is synced.
latestMilestone is the same, but not
latestSolidSubtangleMilestone, your node has seen the latest milestone itself, but not all the confirmed transactions connected to it, so your node is not fully synced. When even
latestMilestone is off, you are probably offline or very badly connected (or connected to badly connected neighbors only, or your node has crashed), as milestones should be broadcast with priority through the network.