Should I use one domain or multiple domains? What is good for my schema and SEO in general?

That depends on the ranking and size of your store. If you are only a starter, we strongly recommend that you stick to one domain only. Until you make it to a larger scale in terms of backlinks, keywords, and content, it will be wise to use only one domain.
Here is a link for detailed information on the topic: https://www.searchenginejournal.com/multiple-domains-pointing-to-single-website-seo/385671/#close .

If you are curious about how a perfect schema structure looks like, you can see the example below..

Remember that you can test your schema by using your product URLs with Google's Rich Result Test Tool: 

Upon testing, please make sure you have only one healthy schema, multiple schemas confuse Google’s parsers, therefore it is highly unlikely that you’ll see your rich snippets such as star reviews, price, and stock info. etc. 

Below is a perfect example where schema is working without errors/warnings.

Please contact our Support and we will be happy to diagnose your schema!