Is it normal to be asking the seller's email when the client is checking out?
No . You should mark it as spam. It’s a scam
SCAM. Do not reply at all!!!! Etsy already has your email; a buyer doesn't need it.
If you already gave them your email, and subsequently get an email from etsy support, it is FAKE.
@IslandCriations: It is a SCAM - you might want to read the excellent post by @bradgoodell in https://community.etsy.com/t5/Managing-Your-Shop/How-to-Spot-a-Scam-No-a-Buyer-Doesn-t-Need-Your-Ema... and https://community.etsy.com/t5/Technical-Issues/Why-do-they-ask-me-for-my-e-mail-in-order-to-make-a-p...
There is also official information from Etsy at https://help.etsy.com/hc/en-us/articles/360000343128-How-to-Handle-Spam-and-Suspicious-Messages?segm...
Be sure to mark the message as SPAM so that it does not affect your stats.