How can I see if the cache on my installed collector is filled?

You can find this information in the collector.log file under the logs (<Sumo_Collector_Home>/logs) directory present on your server.

There should be a line something like "file LogQueue usage: x/y GB (z items), removed n previous items on disk" in collector.log that gives this information.

Sample log line:

2019-09-20 09:14:01,183 +05:30 [Collector Scheduled Executor] INFO  com.sumologic.scala.collector.CollectorDataQueue - file LogQueue usage: 0.00 / 3.00 GB (0 items), removed 0 previous items on disk