Hi, you can definitely use September 2022 GAMSAT for 2023 entry (i.e. applying in Oct 2022); I just did this, but took it Sept 2021 for entry GEM 2022.
The essay part is definitely the most daunting, as you only have 30 minutes per essay and you have to type it (with no function to copy and paste or move text). What I did was went through the past papers on the GAMSAT web site and made a list of the topics. I then decided I was going to write standard argumentative essays, i.e. an intro paragraph, about three paragraphs where I argue for and against and then a conclusion. Once you have this structure, you just need some examples ready to talk about to fit the theme they give you. I found the most useful thing for this was Ted talks - I just read the transcripts of the talks, as it's quicker and my brain works that way - so I created a knowledge bank of examples to use for each theme (part in my head from reading on a train, part on paper when I remembered to add them to my theme list (strongly advise the latter!)). Also, read broadsheet newspapers, articles, actually anything, but always with the thought that can I use this as an example (if so, add it to the bank). Then, practice! Randomly choose a theme and see how far you can get in 30 minutes. I would advise sketching a structure and which examples you want to use, then just go for it. This helps as there is not much time, very little time for any sort of proof reading etc. so you want your structure sorted before you start, and it helps you recall your example in the heat of the moment.
Of course, if you are creative/artistic, you can write poetry, a song, a short story or whatever. For me, that was far too much to think about in 30 mins.
Also, get comfortable with the fact that it is unlikely to be a good essay; you might have good points to make and a decent argument, but you have 30 minutes in stressful conditions to type it up. There is very little time to review, although I would advise trying to leave some ,and if you want to move some text, you just have to type it again. It won't be your finest masterpiece - it just has to be good enough. This thinking really helped me. Of course, you might absolutely nail it, and it's great if you do, but that doesn't actually need to be the aim.
Hope that helps and good luck. Also, plan your food. The exam takes an absolute age from arriving to finishing, so you need to be adequately fed (and caffeinated), with some food ready to go at the break, as you can only drink water in the room (not that you'll have time! Also, make sure you know where you can refill your water or take spares).