Hi Julian,
1. Imagine this scenario: someone sneaks in to your office while you're away and uses your computer to log in to your site. As things are right now, you receive an email notifying you that someone logged in. With a feature like what you requested, it will simply not notify you. I will just say that you can never be too paranoid ;)
2. That, I can do.
3. Not only that would be a very big change, it's a pointless one too. The site's email address should ideally be a no-reply address. You don't want spambots registering themselves as users, finding out your email address from the automatic reply email and unleashing a torrent of spam upon you. Humans, on the other hand, should they need to contact you can always find the Contact Us page on your site. In fact, they can figure out how to contact you even when it's seriously harder than googling the solution to their problem or when the solution is included in the documentation they swear they read "thoroughly" before contacting you. That last bit comes from personal experience ;)
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!