1) Is it correctly to say 'Good day' in the following context:
Good day, dear visitor of our online shop?
Or is it still better to use 'Good morning/afternoon'?
2) Is it better to say that our site welcomes or greets you on the World Wide Web and offers to visit our online shop remotely or virtually?
Which of the highlighted words are more appropriate?
All of these sound very strange.
In an online shop, you don't know if it's morning, afternoon, evening, or black of night where your shopper is.
Simply say "Welcome to the Ksenia Boutique" or whatever your online store is.
It's a virtual store, not a "remote" store, and your customer is an "online shopper," not a remote or virtual shopper.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.