I must be missing something. You asked about mics and lighting - first tehybrid says you need Firewire then NTJetboater mentions LANC cable.
I fail to see how either of those apply to the OP's question. Firewire is a data transfer protocol and LANC is a control protocol. What do either of those have to do with mics and lighting used in production?
And further confusing me is the OP's last question; "Is there a 4pin to 8pin adapter for the light and shotgun mic??" What is it that you are trying to adapt? ... from and to what?
A search for the camera model you listed turned up no results, even on Sony's website. Perhaps you listed the model number incorrectly. But if it's a typical consumer camcorder, it should accept just about any unbalanced mic with the proper connector. Most consumer camcorders have a 3.5mm (1/8") jack for an external mic, either mono (2 conductor) or stereo (3 conductor). See the middle two plugs in this photo:
http://en.wikipedia.org/wiki/Image:Photo-audiojacks.jpg
Professional and some prosumer video cameras used balanced mics connected to a take a 3-pin XLR jack.
Most portable lights made for camera mounting will either have a 4 pin Canon connector for power (only two pins are used for + and - see:
http://en.wikipedia.org/wiki/Image:XLR4_PICT6913a.jpg ) or a cigarette lighter adapter plug, with the exception of a few professional camera lights that are made to power from the battery attached to the camera and interface with the camera's viewfinder. The normal consumer camera mountable light will either have a cigarette lighter style plug or will have a place to attach a battery directly to the light housing.
tehybrid's suggestion for lighting will work in some instances, but not so well if you need to be shooting while moving or outdoors.
That said, some newer consumer camcorders from Sony will only accept Sony accessories due to proprietary mounting modifications. It's Sony's way of selling you more stuff - THEIR stuff. You also asked bout using them at the same time. Is that your way of saying that your camcorder is one of those that takes specialized connectors and/or mounts?
The ECM-HGZ1 and HVL-HL1 that you listed above do NOT list your camera model as compatible. I don't think the C01U mic you listed will work with your camcorder; it's designed to connect to computers and digital audio workstations for direct recording via a USB port.
-DH
also see:
http://en.wikipedia.org/wiki/LANC
and
http://en.wikipedia.org/wiki/Firewire