Are there any problems associated with having a whole house surge supressor, individual surge supressor with backup battery, and standby generator all working at same time?
In my experience, there can be conflicts between individual surge suppressors and backup batteries. However, I see no conflicts between these and a standby generator. In fact, standby generators should be your first line of defense.
You need to look into the technical details and fine print of your backup battery and surge suppressor to uncover potential conflicts, but like I mentioned, I personally have experienced conflict between these two devices. I'm a big fan of generators and have had one for over a decade, and really encourage whole house generators as the first line of defense.