I'm opening a eshop in Canada.
I will sell product both to Canada AND United States.
Will my American customers have to pay the local sales tax for their state?
Is it possible for me to collect them?
I want the buying process to be transparent for the customer (it should not even be able to see he is buying on a Canadian eshop).
Congrats on opening your shop! Since you're based in Canada, I recommend reading TaxJar's blog post on sales tax for international sellers. As for your question about whether it's possible to collect sales tax on Shopify, the answer is yes. I think you'll find TaxJar's Sales Tax Guide for Shopify Sellers to be very helpful!