I edited your post to use proper example domains — please don’t use other people’s private domains. (example.* and *.example are officially standardized and will never be registered to a private company.)
Next, let’s avoid saying “DNS records” as that’s far too general and DNS is very easy to mess up if you don’t understand the different record types. Instead, say “DNS A record”, “DNS CNAME record”, and so on.
www.example.com and www.em.example.com seem irrelevant here. It’s perhaps good to know those names are already taken, but unless you’re sending from username@www.example.com they’re not directly involved in mail sending/receiving.
You seem to be asking:
Q: Can I set up DNS MX records for go2.em.example.com without affecting the MX records for go2.example.com?
A: Yes. The MX records need not even point to the same mailservers, though in your case it sounds like they will.
Q: Can I set up a DNS DKIM TXT record for m1._domainkey.em.go2.example.com without affecting the DNS TXT record at m1._domainkey.go2.example.com?
A: Yes. The DKIM public keys will be different, i.e the contents of the TXT record, but there is no problem having both of these active. You get the DKIM public key from the Admin UI.