JackstrawIII

You came looking for help, so I'll try. Here's how I'd use these rods. 
 
Light 5'6 mitchell spinning: bobber fishing for panfish 
Medium light 7'0 dobyn fury spinning: Dropshot
Medium 6'0 berkely spinning: Ned rig, neko rig, shaky heads, etc. 
Medium heavy 6'0 bionic blade spin: Skipping around docks and brush with texas rigged soft plastics and small jigs. 
 
Medium 6'6 fish eagle RT3 casting: small single hook baits like smaller chatterbaits, paddletails, and such. You could also use it for crankbaits in a pinch, but it's not ideal. 
Medium black beauty 5'6 casting: not sure how I'd use this one 
Medium heavy 6'8 avid x casting: this would be for larger moving baits like spinnerbaits, topwaters, etc. 
Medium heavy 5'6 falcon casting: not sure how I'd use this one 
Heavy 5'6 falcon bionic blade: not sure how I'd use this one 
Heavy 6'6 falcon casting - this is your best bet for things like frogs, toads, jigs, etc. 
 
Ultimately, you'll probably want some longer rods for more power presentations like frogs and such, but you'll be ok for most stuff with what you have... for now. 

I fish a 1/0 for 2.8-3.3" swimbaits and a 3/0 for 3.8-4.3". 

I don't fish bigger than that enough to have a knowledgeable opinion about it. 

This is a big question, but I'll do my best to answer it. Here are the 5 setups I'd use if I had your gear, with the line I'd use in parenthesis at the end. Line choices are very subjective, but I'll try to help at least get you started and will keep it really simple for you, so you only have to buy 3 types of line. I also have never used 13 brand reels and will just choose them based on speed:
 
1. Lews Skipping Rod 6'10 H/F with Lews Skipping Reel (15 pound hybrid line for skipping soft plastics and jigs)
2. 7'4 H/F rod with Concept A2 8.3:1 reel (50 pound braid for throwing frogs & toads & some punching) 
3. 13 6'7 M/F rod with 6.6:1 reel (10 pound hybrid line for crankbaits, topwaters, and jerkbaits)
4. 7'4 MH/XF rod with 8.8:1 reel (15 pound hybrid for jigs, heavy t-rig worms)
5. Abu 6'6 HM/F with 8.3:1 reel (15 pound hybrid line for spinnerbaits, chatterbaits, and smaller swimbaits)
 
This covers a majority of bass fishing. Are there more specialized rods that would be "better" choices for certain techniques? Sure, but this covers all the bases you mentioned in your post moderately well. 
 

Disclaimer: I’m not a pro. 
 
This time of year, the only thing that seems to make a difference is cloud cover. So, if it’s cloudy in the morning, I go then. If it’s cloudy in the evening, I go then. 
 
Low clouds and low barometer are even better.