Can we create new objects similar to products and orders in Shopify and can we get access to those new objects using APIs?
Can we create new custom fields in Customer object and can we access those custom fields using APIs?
I think that would not be possible. However, when scrolling through the list of Liquid objects (https://help.shopify.com/en/themes/liquid/objects) I saw something that could help: the metafield object!
The metafields object allows you to store additional information for products, collections, customers, orders, blogs, pages and your shop. You can output metafields on your storefront using Liquid.
See the details here: https://help.shopify.com/en/themes/liquid/objects/metafield