Yes, c2.dhps.tp.edu.tw can receive emails.
Yes, c2.dhps.tp.edu.tw seems to be a legitimate domain.
A record
None
MX records
ALT1.ASPMX.L.GOOGLE.COM
209.85.202.26
ALT2.ASPMX.L.GOOGLE.COM
142.250.13.26
ALT3.ASPMX.L.GOOGLE.COM
172.217.218.26
ALT4.ASPMX.L.GOOGLE.COM
209.85.233.26
ASPMX.L.GOOGLE.COM
172.253.63.27