Rebrickable has an option to compare two sets, MOCs or combination of both to see which parts are in common and unique to each of set/MOC.
Here is a comparison results between both EV3 Core and retail EV3 versions. You can also spot the "v1" for 31313 set, which means there is more than one inventory known for this set, so this is something you can ...
A year or two ago I got Mindstorms 31313, but I wanted to be able to build the models from the Education Core set too, so I put together a spreadsheet comparing the parts in each.
Here is a Google Sheet with the part lists and the union of the sets: https://docs.google.com/spreadsheets/d/1-bsj9zYrhTREDUyOfGJm83c2htyJIUeL408NDJd_jjM/edit?usp=sharing
Feel free ...
You can try to get them from LEGO pick-a-brick searching for "roof" gives you quite a collection, but misses the ends and corners that are available, so add another search for "45°" to get them.
Combine this with Bricklink and buy whereever it is cheaper or where you can find the wanted quantities of desired elements.
I would suggest to look into buying individual parts on Bricklink in desired color, shape and amount. Any other set you can buy most likely won't have all the parts you need and you are left with otherwise unnecessary elements.
If you really need a set with roof specific parts, the set I could think of now is Emmet's Dream House/Rescue Rocket (70831). ...
Here is a parts list for the CORE SET: https://brickset.com/sets/45544-1/Education-EV3-Core-Set
And here is a parts list for the Toy Robot Building Kit: https://brickset.com/sets/31313-1/Mindstorms-EV3
In the future, there is a good chance that Brickset has an inventory!
Yes, a smart device is required. The box says the following:
Smart device required but not included
However, this set is not like Boost, where the intelligent brick just adds weight to your model without a smart device. Mario functions without being paired to a smart device. He can complete the course, collect coins, etc.
The most significant limitation ...
I would go back and check just to make sure that you have done the last few steps right. If you still can't figure it out, look on either YouTube or Google and type "LEGO 10257 Carousel Not Working correctly". If there is nothing there, contact LEGO Customer Service and ask for help. Good Luck!