Blankwall - Welcome to Nesba!
If you read through the tech requirements in the Riders Manual, it explains what is going to be checked, both bike and gear.
What many of us do is wear the helmet and boots, and put the leathers/gloves over the tank for tech. Since you've got two-piece, you can wear the pants if you like and carry the jacket.
Tech will check the bike for B group checking for:
Any obvious problems with the bike that may cause a problem for you or others on the track
fluid leaks/levels
loose steering head
loose bolts/plastics/things that may fall off
brake levers function
brake pads
tire wear
chain tension
side stand kill switch (if the bike has a side stand)
Lights/reflectors properly taped, brake light disconnected or bulb removed (so it doesn't light)
mirrors removed
Your gear needs to be in reasonably good condition so that you have some protection should you have an off. Again, check the Riders Manual for details
If you are just doing the Intro Sessions, (first two morning B sessions) the requirements (for bike and gear) aren't as strict. See the Riders Manual for details.
Full circumference zips don't actually go a full 360 degrees. What you describe is a full-circumference zip, so you should be fine.
Prepare to have an incredible time! What day/track are you headed for?