Yes, 2-7.design can receive emails.
Yes, 2-7.design seems to be a legitimate domain.
A record
69.163.224.116
MX records
ALT1.ASPMX.L.GOOGLE.COM
64.233.186.27
ALT2.ASPMX.L.GOOGLE.COM
209.85.203.26
ALT3.ASPMX.L.GOOGLE.COM
64.233.184.26
ALT4.ASPMX.L.GOOGLE.COM
172.217.218.26
ASPMX.L.GOOGLE.COM
74.125.192.26