Since F5 doesn't allow us to install our agent on their box, it can get a little tricky to monitor but if you are on version 6.3 or 6.5, you can use the Observed Tiers feature to get some visibility.
More info on that can be found here -> https://community.dynatrace.com/community/pages/vi...
You just need some basic info like Host, IP etc of your F5 Load Balancers and you can have them show up in the transaction flow.
Hope that helps,
No, Dynatrace (Ruxit) and DC RUM are different solutions so the answers for those will be different. Dynatrace Agents go on the OS level and not the JVM like in AppMon so you could theoretically get more visibility into F5.
As for DC RUM, that is a networks based tool which is involved in your data centers so you will definitely able to see what's going on in all your load balancers.
Not sure about Google Search Appliance but if you are able to install an agent on there, you should be good. Otherwise, Dynatrace and DC RUM should be able to provide visibility too.