When making kimchi (or other fermented products like it) it's best to ferment the whole batch together for the first phase (this depends on what you're making, how much of it you're making, and how sour you want it to be - but a week is a good rule of thumb). This helps to make the whole batch more consistent, as one batch will ferment at the same pace - as opposed to many small batches fermenting in different ways - and in general will cut down on variables which is always a good idea when fermenting.
When I make kimchi, I usually make 5-10 liters at a time and put it all into an appropriately sized jar. If there is extra headspace, you have a few options, the easiest of which is to take a clean plastic trash bag, put it into the jar and fill it with water, then tie/close the bag so the water can't come out. This will make it so no oxygen comes into contact with the top layer of kimchi which should ideally be submerged in its own juice at all times.
I leave the jar in a slightly cooler than room temperature room, in the dark (or at least wearing an old sweatshirt so no light gets in) for 1 week to 10 days, then fill smaller bottles and store them in the refrigerator. At this point they can be given away to other kimchi lovers, or kept in the fridge for ~6 months (probably longer, in fact, if they're not opened, but I've never gone longer than that - and in fact it's rarely lasted that long).
In your present situation, I think you'll be fine opening the lids just a bit, but if you're storing them in the fridge there should be no worries at all - it won't continue fermenting in so cold an environment.