Hi,
When you copy a product, the variants can be copied, but for this to work properly, the product code of the variants needs to not be changed from the default.
If you change the product code, then the copy system is not able to match the variants with the characteristics on the copied products and the variants won't be copied over.
The message "No default variant selected." appears when, among the list of variants of a product, no variant is selected as default. So go in the "variants" tab of the product, and on the variants listing, click on the icon of one of the variants under the "default" column.
The message "The product has characteristics but not variants. Click on the 'Variants' tab and add variants to it." appears when no variants are linked to a product. So you need to go in the "variants" tab of the product, and click on the "add variants" button to add new variants.