Is the kimchi still okay

I'd strongly suggest succeeding on the small scale first, but you can do what you like. Metal garbage can with plastic liner sounds like a terrible idea (plastic liners always seem to get leaks, and then you have acid in a metal garbage can...) Disclaimer - I have two quart canning jars going right now. Depending how they go, I'll consider a larger batch in the later fall, or just do some more quarts, or call the experiment a small investment in not wasting more time/ingredients if I don't like the results, or need to adjust my process before scaling up.

For big, cheap, available, sealable and hard to break you can't beat a "brew bucket" from a beer homebrewing supply place - it's food grade plastic, it's set up to use an airlock, and you can buy an airlock there if it doesn't come with one. Or you can find a cheaper or free used food grade bucket (or even barrel) somewhere else and clean it out really well (hot water and baking soda are good for removing the smell of what went before.) Then get an airlock and stopper at the homebrew place and drill a hole in the lid for it...and find a plate that fits down inside it for a weight.

If you are sufficiently offended by plastic, there are the traditional kraut/pickle crocks (including US made ones, which at least means it's been shipped a bit less, for my location) and there are also larger glass jars (just keep any glass jar in a dark place.) The traditional crocks tend to include weights to keep the cabbage below the brine and an airlocked (generally by water-filled trough) lid. For other containers you can either improvise those or purchase accessories for a non-improvised approach.

Other than that, be sure everything (including your hands) is clean (and for the container, effectively sterilized is nice) weigh your cabbage (or cabbage and...) and add 2-2.5% salt (kosher, pickling or otherwise non-iodized and additive free) by weight. It's useful to stir the salt in and then leave it alone for 30 minutes or so - some recipes go on about "massaging" the cabbage, but 99% of making brine from cabbage is salt, osmotic pressure, and a little time to work. You can stir the salt around once and let it do the work for 30 minutes while you do something else, or stir and "massage" for 30 minutes - the result is pretty similar. Unless the cabbage is dried out, you should not need water to make sufficient brine. Some means of keeping the cabbage weighed down is needed (as it makes gas during fermentation it wants to float) but if you are using an airlocked container there is no need or benefit (and, in fact, the opposite of benefit) to opening the container up to look for quite some time (6-8 weeks) unless you are after less than fully fermented sauerkruat - just keep water in the airlock.

"open-crock" instructions will have you scraping mold off the surface and washing the weight (plate, usually) every few days, but that's because an open-crock situation is exposed to air on top - a sealed/airlocked fermenter (crock, jar, bucket or whatever) is filled with carbon dioxide as the ferment starts and air is not allowed back into it, so spoilage on the top is not so much of an issue (though floating cabbage still won't ferment properly, as I understand it.)

One seriously low-tech airlock method is plastic wrap (it won't be touching the food) and a rubber band on a glass jar. Stock canning jars lids and bands, if properly adjusted to "fingertip tight" will release excess pressure just as they do in canning (and as in canning, if overtightened they will bulge. Canning lids twisting )

Patience. Unless the weather is quite warm, a week is a more typical minimum fermentation time; three weeks if you use a refrigerator method.