2010 Honda Odyssey rear rattle and engine light

Yes, it looks like it 2005 to 2010.

2005 2006 2007 2008 2009 2010 HONDA ODYSSEY ...

eBay https://www.ebay.ca > ... > Sunroofs & Parts

2005 2006 2007 2008 2009 2010 HONDA ODYSSEY SUNROOF MOONROOF ASSEMBLY ; Quantity. 1 available ; Item Number. 283729222605 ; Brand. HONDA ; Accurate description. 4.7.
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More here

https://www.google.com/search?q=2005+Honda+Odyssey+compatible+with+2008+Honda+Odyssey+moonroof

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I would read 'Back Up' as reversing lights and camera if equipped.

Fuse Box Diagram Honda Odyssey (RL3/RL4; 2005-2010)

https://fuse-box.info > honda > honda-odyssey-rl3-rl4-...

The interior fuse boxes are located under the dashboard on the driver's and passenger's side. The location of the fuses in the passenger compartment: Honda ...

Honda Odyssey (2006 - 2007) - fuse box diagram

https://www.autogenius.info > honda-odyssey-2006-20...

May 14, 2017 - Primary engine compartment fuse box ; 1, 10, Left Headlight Low ; 2, 30, Rear Defroster Coil ; 3, 10, Left Headlight High ; 4, 15, Small Lights.

https://www.google.com/search?q=2006+honda+odyssey+fuse+15

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What Ray said. Agreed.

Did you change out the thermostat? I would also change out top and bottom radiator hoses if they feel soft. They should have firm sides.

You need to find out what that rattle sound is.You mean after the car is turned off? I would also buy a quality battery. Not from Walmart.

check the main engine fuse also the fuseable link, when fixed, buy wife a bicycle with a carry basket on the front

I can’t be much help on this one (too new for my experience), but your manual will say this (which probably isn’t all that helpful either).
The vehicle stability assist (VSA) system helps to stabilize the vehicle during cornering if the vehicle turns more or less than desired. It also assists you in maintaining traction while accelerating on loose or slippery road surfaces. It does this by regulating the engine’s output and by selectively applying the brakes.
When VSA activates, you may notice that the engine does not respond to the accelerator in the same way it does at other times. There may also be some noise from the VSA hydraulic system. You will also see the VSA activation indicator blink.
The VSA system cannot enhance the vehicle’s driving stability in all situations and does not control your vehicle’s entire braking system. It is still your responsibility to drive and corner at reasonable speeds and to leave a sufficient margin of safety.
On touring models you will also see a ‘‘CHECK VSA SYSTEM’’ message on the multiinformation display if there is a problem with the VSA system.
Without VSA, your vehicle still has normal braking and cornering ability, but it does not have VSA traction and stability enhancement.
The VSA system automatically turns on every time you start the engine, even if you turned it off the last time you drove the vehicle.
I’d get on the Honda people about the problem, especially since you just got the car. I would think that the alarming sounds you are hearing have to do with the unit working the brakes when it shouldn't be, but that's a guess.
Hope this helps some.

a clunking clanging noise sounds very much like your stabilizer bar end links and bushings. you have a thin rear "sway" bar on the rear of your odyssey. this can cause a whole lot of noise. grab each side and pull/push. if it feals loose, replace the end links and bushings.

is your ac compressor located on the left side as well and also try your ac if its not blowing to cold the rattling could be your ac clutch on the compressor if that is you will have to get a new clutch kit from your local auto parts store to fix it

the heat shield on the exhaust manifold