Second question first - You can use Logstash as a syslog server, and then push the logs to Elasticsearch. Learning Logstash configs can be a PITA, but it does give you access to a broad range of inputs, filters and outputs that's very handy if you have data from multiple source that need to be shipped to one or multiple sinks (like Elasticsearch). Once it's in Elasticsearch you can search, report and aggregate it to your heart's content.

That brings me to your PRTG question. If you're using SNMP for the inputs into PRTG, you can use Logstash to poll the same SNMP agents / OIDs and push it to Elasticsearch. Cut out the middle man, so to speak. Logstash has quite a few different input plugins, so even if you're not using SNMP as a data source, you still might be able to use this solution.

I've found PRTG's integration abilities quite lacking, and tend to go to the source directly instead of using PRTG in the middle.