How the upsells work with variable products, products which have many options for customer to select from?

If I have the variable product as an upsell, which has plenty of variations and options, are the customers able to select their size and color (or other options) on the upsell page? or is it just one variation?

You just need to select the parent product in “Product to offer” field.

If you will set “Display offer method” to “default page”,
then the product option select boxes will show up automatically
on the upsell page, for customer to select them.

If you will set “Display offer method” to “custom page”, then you need to add a shortcode “[wc_1cu_variation_selector]” on your custom upsell page. Also you need to wrap your Yes / No buttons or links with

in order for variation data to be passed properly to the upsell order.