Use Apple Time capsule as NAS for Sonos

"Would my iMac need to be on?"

Since iTunes is on the Mac and only the data is on the Time Capsule, yes the iMac would have to be on in that configuration to serve up the data to the Sonos.

"Or do I need to buy a WD Personal Cloud wireless hard drive and just buy an Apple Extreme wireless router"

That would be same as have the iTune library on the Time Capsule.

1. Buy the Time Capsule to use as a NAS hard drive

Yes, you can use a Time Capsule as a NAS but it would be more efficient and better performance-wise to use a dedicated NAS instead.

2. Change my iTunes library to be resident on the Time Capsule hard drive and NOT on my iMac anymore.

Yes, that would work. As you may already know, iTunes uses two components: 1) iTunes Media Folder, i.e., where the actual source files are located, and 2) the iTunes Library. Basically a catalog of what is in the Media Folder. Both are required for iTunes to work properly. However, they can be placed in different locations.

4. Question: would the Time capsule hard drive show up as a mounted drive on my wireless network. If so, then I could point the Sonos app to the iTunes library

When sharing is enabled, the Time Capsule's presents its internal hard drive as a network drive. Also any attached USB drives will be shared out as well. Sharing is enabled by using the AirPort Utility.

5. Would my iMac need to be on?

If you plan on streaming from iTunes then the answer is yes. That is because the Time Capsule is NOT an iTunes server. This is where dedicated NAS devices, like the Synology DS414, really shine as they offer this server service.

So does the Sinology DS414 have the software to let it be an iTunes server and all I need to do is copy my iTunes Media folder to the NAS?

iTunes server is part of the DiskStation Manager software that is the basic operating system for the Synology NAS devices ... so, yes and yes.

Link below explains how to set up an Apple Time Capsule with Sonos.

https://sonos.custhelp.com/app/answers/detail/a_id/694/~/setting-up-an-apple-tim e-capsule-with-sonos-on-a-mac