Help with back up issues?

Here's overview of my iMac, 27' late 2012, 3.2 GHz Intel i5, 8 GB, 1tb, Graphics NVIDA GeForce GTX 675MX. Seagate Expansion Portable 2TB
Have but not yet used- Apple Time Capsule 802.11n WiFi and a Thunderbolt storage dock w/2 spots for SSD or HDD I have 256GB Samsung Evo I installed into Mac Pro via a PCI-e expansion card but since iMac is going to be my main editing I'm going to use SSD with Thunderbolt since I don't want to chance opening iMac up.

I need advice as to how to remove previous backups from my 2tb Seagate expansion external hard drive. I'll try to explain the situation as best I can... Last Fall I bought my first Mac a 13" MBP w/Retina and the above external hard drive which I formatted since I hadn't realized it wasn't for Mac. Seemed to work fine but since I'm still new I'm not sure if I really set it up right or not? In September I sold my MBP because I wanted something to run Abobe CC for Photography with a large monitor and couldn't afford both, got a deal on a Mac Pro 3.1 w/30" Apple monitor and my personal late 2012 27" iMac (one in question now). After installing Lightroom and Photoshop I plugged in my Seagate and tried to delete some older photos but I get this each time I try "The operation can’t be completed because backup items can’t be modified." I've been able to import with Lightroom but still occasionally run into the same permissions issue when editing? I tried to follow suggestions I found online for example changing the "sharing & permissions" but the main suggestion about checking the box to remove permission isn't there on my iMac? I've tried to add my name since I used the short version of my name on the Seagate and long version when I set up new Mac but it's not working either?

Another thing I need help with is best steps to take when I set up a new Time Capsule 802.11n WiFi as I'd like to use it as an additional backup for both machines as well as Network drive. Directions tell me to use ethernet for first backup but since theres really nothing on iMac yet is that needed? Plus should I set up the Network or backup first?

I ordered a HighPoint RocketStor 5212 Thunderbolt Storage Dock to put a Samsung Evo 250gb SSD into but am not sure how to use it that will give me the best results. Should I use it to run my OS or what would be the best Photo edit set up for me keeping in mind I have an additional spot to add another SSD or HDD? As of now it takes awhile for it to load up and last night the first time I've used Photoshop it really seems slow taking forever when I was using refine edge.

I realize I've asked a bunch of related but different questions and appreciate any and all advice.

Thank you in advance;-)
Tina