domain name system - DNS trouble - think it might be caused by two NS records

About a week ago, I updated my DNS, adding:

HOST, TYPE, VALUE, TTL
*.soup-team.com CNAME www.myopenid.com 3600
mail.soup-team.com CNAME ghs.google.com 3600

HOST, TYPE, VALUE, MX, TTL
soup-team.com MX aspmx.l.google.com 10 3600
soup-team.com MX alt1.aspmx.l.google.com 20 3600
soup-team.com MX alt2.aspmx.l.google.com 20 3600
soup-team.com MX aspmx2.googlemail.com 30 3600
soup-team.com MX aspmx3.googlemail.com 30 3600
soup-team.com MX aspmx4.googlemail.com 30 3600
soup-team.com MX aspmx5.googlemail.com 30 3600

From before, I had:

HOST, TYPE, VALUE, TTL
soup-team.com A 64.120.188.121 3600
soup-team.com NS ns01.000webhost.com 3600
soup-team.com NS ns02.000webhost.com 3600
www.soup-team.com CNAME soup-team.com 3600

Additional details:
The domain is purchased from www.proisp.no
www.everydns.com is used for DNS management.

Now, from home, everything works perfectly, but from the university, neither mail.soup-team.com nor any of the OpenID-related subdomains are working. Instead, an error-message from my webhost (000webhost), is displayed - err.000webhost.com.

I've used OpenDNS's CacheCheck (www.opendns.com/support/cache/) to check their cache as I thought this might help me identify the problem. After requesting a refresh (yesterday, and today), all of their caches point correctly to mail.soup-team.com and most of them to the OpenID-related subdomains (which caches are not updated seems to differ for different usernames).

I have a theory that the problems might be related to some caches ignoring the *.soup-team.com rule and instead querying the 000webhost Name Servers.

So, my questions are:
1) Have I made any sort of misconfiguration?
2) Since I have an A record pointing to the IP of 000webhost, and I'm not using their subdomain option, can I remove the NS records (ns01.000webhost.com and ns02.000webhost.com) without causing other kinds of trouble?

Thanks in advance,

method139

PS: I'm quite new to DNS. If I'm using the wrong words to describe something in this text, I'm more than happy for any feedback related to that as well.