Email me at or reply to this email?

1. How do you professionally say reply to my email?
2. Do you respond or reply to an email?

How do you professionally say reply to my email?

Some words such as “Thanks for the email!” is polite enough. You also can write a thank-you sentence and another closure such as Yours sincerely, Best Regards, etc.

Do you respond or reply to an email?

"Reply" is probably better when you're texting your friends like, "Please reply to the invitation by tomorrow." Sounds much more natural. "Respond" would be good at work when you're using like work email for something or when you're on the phone as well. Using this is much better for business situations.