Will a battery be damaged when in series with a low frequency AC signal source?
Imagine the 5V voltage source as a battery. If I place it in series with a signal generator will I ruin the battery? Also is it safe to place the battery and the signal generator in parallel?








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The OP's circuit redrawn.

If we redraw your circuit we can see that the there can be current flow in and out of the battery. 


When V2 &lt; V1 the battery will be discharged at a rate of \$ I = \frac {V1 - V2}{R1} \$. This should be OK.
When V2 > V1 the battery will be charged by V2.
Whether this is safe or not depends on the battery chemistry (is it rechargeable) and the safe charging current. 



  Also is it safe to place the battery and the signal generator in parallel?


Again, you it depends on the voltages. 


If the signal generator has a decoupling capacitor on the output then


On initial connection it has to be able to survive the DC kick back through the capacitor.
The capacitor has to be rated to withstand the DC voltage.

If there is no decoupling capacitor then the output stage has to be able to survive driving into a current sourcing load.


Are you still trying to solve https://electronics.stackexchange.com/questions/246694/earth-fault-monitoring-system?