Electricity doesn’t inherently cause fires. Electical fires are caused by heat created by short circuits or other failures that cause short circuits where the resistance of the materials being heated aren’t destoryed before they create enough heat to cause ignition of the surrounding materials. You’re dealing with fairly low voltage/low amperage devices that have very little risk of fire inherently. Each of your devices are designed to manage their own power against failures.
If you have concens and want to allay them, as noted, make sure your eletrical outlets are in good condition and that your power strips,etc. are in good, working order. (Also make sure your patch cables keep away from outlets, but that’s more of a health risk than a fire risk.)
Which is to say, just because you have a bunch of devices and lot of wires you can see, there’s no significantly increased risk of fire. They’re just standard electical applicances and pose similar risks to the other appliances that you already have around. Most failures merely destory the functionality of the appliance, not the things around it.
Think of it like starting a fire in a cold fireplace; in order for the wood to actually burn, it (and the material around it) has to be heated long enough and to a high enough temperature for there to be enough heat for the material to begin combustion.
If you wish to be 
certain, just unplug your system when it’s not in use.
