Foot off the clutch = rattle
Foot press cluth = no rattle
Foot let off clutch start to drive first gear = squeek


What is the problem?

 

I would focus on two things.

1) get a sound clip of this for us or upload a video to youtube. Can't asses noises very easily by description.

2) focus your efforts on the squeek. I cannot tell for sure not being able to hear it, but your first two items with the rattle are probably the normal rattle for this car. And then not only is it possible that the rattle is normal and the squeek is not but they are totally unrelated then. Focus on finding the source of the squeek only for now until you can get a way for us to hear it too or get a mechanic to inspect the squeek.

 

Even quicker is to eliminate the rattle on your own. Search(!) for clutch rattle and find the dozens of other people who have already asked about this noise and did provide sound. See if their sound matches yours! Much easier than recording yours and adding to the long list. Get this one out of the way fast and move on to the squeek.

 

If by rattle you're referring to clutch chatter at idle then that is normal for the Z, sounds like a small cement mixer. Bump your idle to 850-900 and you'll rarely hear it .
Squeak when feeding the clutch in first gear to get going may be normal depending on your clutch set up, mine has been squealing for like ever now. I never quite narrowed it down , may be disk material, slave cylinder (if you have an HR with the Internal slave) , or maybe even the pilot bushing.
Unless of course your squeak is the actual clutch pedal itself then just lube that b!tch up lol

 

My clutch pedal was squeaky for months and drove me crazy. I lube'd it like crazy with and it never went away.

Finally fixed it by putting brake caliper lube on the spring beneath the clutch. It takes a few hours of driving for it to get completely worked in, but it's nice and quiet now!

 

^THIS

I used Dupont Teflon Lube and it worked great. At first I sprayed it near the plunger, drove around and still heard it. Afterwards, I worked it into the spring and its quiet now.

 

The rattle is normal the squeak needs wd 40 (or Teflon). WD 40 will last about six months.