After living here for almost half a year, here are some of my thoughts:
Apple Pay and Google Pay are extremely popular in Melbourne; so far, I haven't encountered any place where you can use a card but can't use Apple Pay. QR code ordering exists too, but it's not common, mostly found in Asian restaurants. After scanning, it opens the restaurant's own website, where you order and pay (though some ask you to pay in-store), and the receipt is sent to your email. Many cafes and restaurants have their own websites, complete with contact information and menus.
Regarding e-commerce: besides eBay and Amazon, there are numerous e-commerce websites, each with its own account system, order system, discounts/special offers, etc. When looking to buy something, it's necessary to compare several websites for prices, including discounts, coupons, shipping fees, cashback, etc. Some platforms support Price Match, meaning if you find a product cheaper on platform A than on platform B, you can try contacting customer service to purchase on platform B at platform A's price.
About shipping: for items ordered from Amazon, unless they're from another country, most can be delivered within 3 days. Other platforms generally use AusPost, similar to China Post. Most packages also get delivered within a week, depending on where they're shipped from, with same-city deliveries usually arriving the next day or the day after. There's no delivery service on weekends.
Every household has its own mailbox, which is very important, and needs to be checked regularly. For example, bank statements, terms changes, government letters, licenses, etc., are all delivered by mail. Some companies even make their mail very fancy.
Email is very common, for communicating with customer service, logistics notifications, discounts/promotions, communicating with rental agents, bills, receipts, and so on. Thus, efficiently managing your email is very important. This is because extremely important information and advertisements are all mixed in your emails.