Will creating the DC (and by extension, domain Y) on domain X cause any issues?
You cannot have a domain controller for one domain as a member of a different domain. Domain controllers, in effect, are the domain for which they're on.
Will these two domains conflict with each other if I don't initiate a trust relationship between the two?
The domains will effectively not be able to talk to each other, unless and until you establish a trust relationship.
Frankly, these are pretty basic questions that you have, and if I were you, I'd lean on consultant, or a more senior colleague with relevant experience. With your level of knowledge, you're begging for a disaster trying to set this up (and do a migration) yourself.
At a very minimum, you need to educate yourself on Active Directory. You could start with the excellent thread by @MDMarra that we have here.
on domain xdo you mean on the same network? If so, then there shouldn't be any problem. Just make sure you don't have conflicting ip addresses or NetBIOS names. – joeqwerty Jul 24 '14 at 20:33