The icon will now appear in your Mac's Dock. If it doesn't appear immediately, check your Applications folder in Finder and drag the new icon down to the Dock manually.
Yes, in Chrome or Edge, click the three-dot menu > "Save and share" > "Create shortcut." This creates a desktop icon. You can also drag the lock icon next to the URL to your desktop. how to pin a website
The icon appears on your home screen like a regular app. The icon will now appear in your Mac's Dock