yes you can point to same server whatever domain amount you have. Only 1 thing you need to know is check with server helpline and ask them all other technical question and 2 domain is not a big issue to host from same server
your web hosting plan, does it support parking multiple domains? did you check your hosting plan? if it does then it is possible. Park your domain on different folders to have them as a separate website. You had mentioned thread title as DNS issue but this is not an DNS issue, you could take help from site ground for parking your domains.