VLAN Setup using a Switch

Hi there…
I have a network with real (class c IP addresses) and private ( class A IP addresses).
I need to separate the traffic of these two
networks using VLAN technology.I have a switch which supports VLAN.It has 24 ports and can be devided into a maximum of four VLANs( I only need two).
Can I just set up the switch to have two VLANs with one for each network ( class A & c) ?
Do I really get two Virtual switches in this case with separate traffic for each ?

Can I just continue to use my switch while mixing class A & C IP addresses on the same physical segment ( No VLAN ) ? Any Problem with this design ?

Please try to answer my question ASAP.
Thanks & best regards.