User Registration Confirmation (not email)

Good day!

I set my user registration to be auto-confirmed upon registering to my site but after my users register, the registration form reappears and there is zero confirmation that the registration is complete. Further, the email confirmation is not coming through.

So:

1) How to solve a registration confirmation on the webpage after users register?

2) How to solve email not sending? (I know this is an ongoing discussion but is it solved?)

thanks!