Are you sure there's enough space in your head for that toilet? The "standard" bowl is 19.25" front-back...the "elongated" bowl is 21.5"!
I am using my deck wash pump to deliver raw water to the toilet through solenoid valve.
That won't work
The solenoid ONLY controls pressurized flush water from the onboard water supply. It can be compared to a faucet...opens to allow water to flow to the toilet, closes to "turn off" the flow of flush water. It can't turn a pump on and off.
The remote pump (your deck wash pump) ONLY brings in raw water. It's a completely separate flush water intake system from the pressurized fresh water flush. It doesn't use a solenoid, but it does need the vented loop in the line between the deck wash pump and the bowl.
Do you think I need to connect output from solenoid valve through existing vented loop or run it straight to the toilet?
You'd only use the solenoid at all if you're also planning to have fresh water flush. That line would go straight to the toilet.
If you're NOT planning to have fresh water flush, IMO you're buying the wrong toilet...paying for features you can't use ("smart flush" panel, for one thing) just to get a bowl style .
Here is a link to the installation, operation and maintenance guide for the A-Freedom:
Raritan Atlantes Freedom owners manual
I think you need to spend some time with it. I'm open to a Skype call if you think we need to talk.