First Sonos System

Welcome!

No, the proposed system will not work the way you want. The Arc already has right, center, and left built in to it, there is no way to separate that out to feed the extra front speakers. 
 

You can only have a single pair of speakers as your rear surround speakers, bonding an Amp to the Arc would achieve that, although general wisdom is that ceiling speakers are not necessarily the best for that, since the ambient sound from surrounds is really designed to be at ear height. That being said, there are many who are pleased with that setup, so it’s worth a test to see how you like it. 

The Arc, with a pair of surrounds, an a Sub (or two, or one mini-sub) is all you can place in a Sonos Home theater ‘room’

If it were up to me, I would just set up the Amp powering those wall speakers as a separate ‘room’ and use them just for music. If you tried to ‘group’ them with the Arc, while playing input from the TV, there would be a minimum of a 75ms delay between the two rooms. However, grouped while streaming music would be wonderful. 

So you can only bond 1 amp to Arc?  What about not using the Arc and only using the in wall/ceiling speakers with the subs? I could also position a pair of the in-wall speakers behind my one side of my couch at ear level, would that help?  

Yes, you can bind one Amp as surrounds to an Arc. 
 

You could replace the Arc with an Amp, which would drive your stereo pair of speakers, and then get a ‘faux’ center channel created by that pair. You would then bond the second Amp to the first to get the surround channels. 

Sonos doesn’t make any situation in which you can have a disparate center channel speaker, all of their solutions either include it in a sound bar, or as a generated channel created by combining signals from the right and left speaker. 

Take a few minutes to read this area of the forum, you’ll find dozens of requests like yours, all with similar answers like mine. 

Sonos is great for dual use, music and HT, in a "normal consumer" like set up. For a dedicated theater room I'd choose a dedicated HT receiver and speakers, maybe binding them to Sonos speakers elsewhere in the house through a Sonos Port.

Which option is going to sound the best?  The Arc with rears only or the in walls and ceiling both powered by amps?  Will the subs work without the Arc?

You say you already have all these speakers.  Are they wired and installed or you’ve just purchased them but they are still in box?

Sonos is a wireless multiroom audio system first and foremost.  Secondary, it’s a home theatre system for people who can’t setup wired systems for various reasons.   It sounds to me like your trying to use Sonos more like a traditional wired home theatre system.  Since you have access to put wires behind the walls and ceiling, why not use a traditional wired home theatre system?   Seriously, I think Sonos is great, but it’s not right answer for every situation,  If you want wide stereo front speakers, separate center channel, atmos ceiling speakers, and rear surround audio, then don’t use Sonos for this.

You can connect a Port to whatever system you setup so that it can play in sync with whatever Sonos you have in the rest of your house.

And, to answer the specific question, the Sonos Sub requires being “bonded” with another Sonos speaker, it can’t exist by itself, or work with another company’s speakers. 

If you want to be able to enjoy Dolby Atmos you’ll have to go with the Arc and any combination below for the ultimate sound:

Sub Gen3 x 1 or 2

The above Sub(s) with Era 300 x 2 as surrounds

You could start with Sub(s) and add surrounds later or start with surrounds and add Sub(s) later

If you don’t care about Dolby Atmos you could use in-wall  speakers up front powered by a Sonos Amp and in-ceiling speakers positioned over the seating area for surround powered by a second Sonos Amp.

Honestly, I don’t recommend the in-wall nor in-ceiling setup unless there is a compelling reason. I haven’t read that being voiced in your query.

I suggest you explore alternative use for the in-wall and in-ceiling speakers or return them.

Everything is brand new in the boxes.  I was gifted 85% of the items and purchased a few myself.  I don't think I can return the gifted items.  I have a few locations already pre-wired and can wire up another location or two if needed.  First time using Sonos and kinda surprised I can’t create whatever system I want.  I would think with the amps I create my own pairs, etc. 

Would a better option be to use Era 300’s as the rears?