Some would say that "allow_url_include = on" is a dangerous setting if you're running PHP code that's not properly sanitized (the latest version of Zen Cart is safe from those risks, but that doesn't guarantee that any other scripts you've got on the site are safe).
Additionally, "register_globals=on" is also considered poor practice from a security standpoint.
While your hosting company may feel defensive about this comment ... "safe_mode=on" is indicative of a hosting company who is paranoid of security matters and just turns on a catch-all option which cripples all kinds of functionality, rather than taking the time to carefully fine-tune and secure the server.
As well, some would say that the fact that they've added suhosin suggests the same paranoia. Suhosin shouldn't harm PayPal communications, but it will certainly prevent you from being able to use the whos-online viewer in the admin area to see customer shopping activity in real time.
OpenSSL 0.9.7i 14 Oct 2005 is a little newer than what your server is apparently using: OpenSSL 0.9.7e-p1 25 Oct 2004
Granted, the above items should have no impact on PayPal transactions, unless of course Safe Mode is configured with poorly-chosen restrictions.
And further, none of the above issues is related to name resolution on the server.
Frankly, if your hosting company can't figure out how to get name resolution working properly on their server, you should be taking your business someplace where they know what they're doing.