Yes it will work without the hdmi but its better quality with it that's all. It has the basic coax cable hook up as well also the yellow/red/white hook ups also.
Yes, you can screw a coaxial into it to receive a cable signal. However, using the HDMI cable, which is available through your cable provider or you can purchase one, enhances the HD channels. If you do not have HD cable, you will not be able to take full advantage of the picture quality.