Using Your Head(space)
For primary fermentation, Master Vintner kits ask you to use an air lock immediately after pitching the yeast. Some sources (mostly on the internet) say not to use a closed fermentation with an air lock since yeast requires oxygen for a vigorous start. It is true that yeast can use oxygen during the anabolic, or growth phase of their life cycle, and a dose of fresh air will speed up the onset of alcohol fermentation. But that's not the whole story.
The yeast cells in the packet of beige powder you pitch into the juice will make only a tiny amount of alcohol in their lives. That's because in a wine fermentation yeast works in distinct stages. In the beginning, they don't make alcohol--in fact, given the choice, they'd never make a drop of alcohol because it's a waste product that eventually makes their environment unliveable.
Instead, a yeast cell’s first priority is to breed new daughter cells. To do that they need to build up new membrane (cell wall material), because they 'bud' new daughter cells by blowing a bubble off their body and then popping it off--poof, instant inflatable kids, and the mother cell has a round scar like an acne blemish to show off.
Yeast can grow their membrane two ways. One pathway uses oxygen, so getting some air into the must can help the yeast breed quickly and get the fermentation on its way to a clean and complete finish. However just leaving the lid off won't contribute any oxygen because once the yeast starts any breeding activity they gas off carbon dioxide and blanket the top of the wine, excluding air contact.
All commercially cultured yeast is grown in high oxygen/low sugar media so that they develop all the membrane precursors they can use. That's why most wineries use cultured yeast instead of wild fermentations: cultured yeast work well without the danger of exposing the wine to excess oxygen. The package you sprinkle on your kit has fit, buff and eager yeast, ready to breed up to culture strength.
The other way to grow new membrane uses YAN (Yeast Available Nitrogen) and other nutrients in the juice. It's independent of oxygen uptake and works just fine. Master Vintner kits have a nutrient cocktail added directly to them before they are packaged. This isn't a kit thing, it's the same process that commercial wineries use. These nutrients ensure that all of the good stuff for the secondary pathway of making new cell membranes is at the peak amount--not too much, not too little, and it ensures that the yeast is vigorous and hardy.
So, headspace or no? It's not important to the yeast, since they'll be doing just fine with their YAN, and gassing off CO2 which protects the wine from oxygen, On the other hand, you need space for the inevitable foaming that's going to happen, and a sealed fermenter with an airlock will keep out stray fruit flies and any other contaminants from entering the wine.
After you've racked from primary to secondary there will be a headspace of around 1.25 quarts in volume, but that's okay because the wine will still be fermenting and outgassing CO2, which will protect it from oxygen. After you've fined, stirred to degas, and added your sulfite and sorbate, your kit will sit approximately one to two weeks to clear.
During this time, the headspace will be filled with the last of the carbon dioxide coming out of solution. It will also be protected from oxygen by the sulfite, which reduces the oxygen and binds it out of the way. In that short time, your wine won't oxidize or change character in any meaningful way.
Here's where headspace becomes an issue: if you're going to keep the wine for longer than the specified clearing period, then you are obligated to top up to eliminate headspace and prevent oxidation. You can't rely on the airlock to keep oxygen out, as the seal on the bung will allow oxygen transfer into the wine--it's less than a 16th of an inch of rubber against the neck of the carboy, so it's not a great barrier to oxygen. Topping up prevents oxidation because it reduces the surface area of the wine inside the carboy that can soak up air. If the wine is down the shoulder of the carboy, the surface area is the same size as a dinner plate. If it's topped up right into the neck, just below the bung, it's the size of a 50-cent piece, and will soak up way less oxygen.
Don't use water to top up: you added all of the water you needed on day one. Instead, use a similar wine. How similar? Use a white for whites and red for reds, and dry for dry, sweet for sweet, oaked for oaked, etc. If you followed the instructions, it will only be a bottle or a bottle and a half of wine. Then you can leave it sit, topped right up into the neck, to reduce the surface area of the wine that's exposed to the atmosphere. Keep your airlock topped with water or switch to a solid bung and you can store it for another month or two without any trouble.
Beyond that, the best place to store wine for aging is inside wine bottles--that's where all the wineries put their vintages to age over time.
Well, maybe it's the second best: storing it inside a thirsty winemaker is a pretty good idea too!