First off, a little about myself: I'm diagnosed with Asperger's myself, and i've worked in software and IT for nearly a decade - that is including some long-term unemployment (a little over 2 years has been the most for me).
With that out of the way, i'll take it from the top.
I have a bachelor's degree in Journalism but chose not to further pursue that. Instead I followed a traineeship as a Java Developer in 2016 where I got my Java 8 OCA cert, followed by 10 months of work experience as a junior developer.
You have a certification and less than a year's worth of experience - with that in mind, how does your resumé look otherwise. Have you had a lot of short-term jobs?
Most of the places i've worked at, i've been at for a little over a year at most. Most companies want to see that you can commit for a longer time than that.
Aside from that, you mentioned that you asked for a 32 hour work week. Are you still asking for that?
Most companies ask and often need someone in software or IT to be able to commit to a full work week and even overtime, especially when it comes to jobs that where deadlines are a big part of the development schedule, like web dev bureaus, consultancies etc - they want a lot of work done in a short timeframe, and often include customer-facing support as part of the job.
Your best bet could be in a company that doesn't do software development as its main role, as an internal programmer.
In the meantime I have been working on myself as per everyone's advice, but this has not made it easier to work on my career. In the past 3 years I have worked on my programming skills, though this is obviously not enough. So far I have created an Android app and published this, learned the basics of pen-testing and followed a couple of tutorials here and there, but I'm finding it hard to pick any one thing, as I'm not sure if what I'm learning will help me advance my career.
You do have your Android app as part of your portfolio - make sure to mention in an interview what you have done with it, learned from it and what your experiences have been. Having something to show off as a programmer is better than nothing.
Being able to pen-test and do IT-related forensics is a nice skill on paper, then again it doesn't stand on its own - to be a good pen-tester (or hacker for that matter) you need to be well-versed in multiple programming languages, hardware, security practices, observation and social interaction.
I'm not saying it's impossible to pursue that path as an autist - on the contrary it's a good way to face the shortcomings that many autists have and combine it with their strengths.
I am unsure where I stand. A lot of people have told me that with my resume I should be able to get a job just fine, but personally I feel like I might be arrogant in thinking I stand a chance, especially without an IT-related degree and so little work experience.
We've all been there - even with a degree and experience it's tough to get a job. However, it's worth mentioning that it's not because of you - it's because software development is a job market that is oversaturated not only by other prospecting software developers, but also by literally a million different systems, APIs, paradigms, languages and ways to handle projects.
Feeling arrogant and unsure about your own skills is something that happens to everyone in the face of a flood of rejections. It's worth mentioning that the paperwork and interview cannot in any way gauge your actual skill. They stand alone as a way of figuring out who you are and how you work. You may get a test on writing a fizz-buzz program or something similar - but it too doesn't gauge your actual skill.
Remember always: You have the skill and competence they seek - they want to know how and if you can actually apply that skill. You have an app and (hopefully) some numbers that can prove it.
Tailor it to whomever you are speaking with at the interview - If it's the CTO or someone from the tech department, they usually want the technicalities. On the other hand if it's HR or the CEO, they want numbers and your personal (or "soft") skills.
So with that as my background, my question would be: what are my options?
It does depend on your age. If you're young, you still have the option of seeking out other paths. This is something that has been on my mind as well - there is the option of taking jobs that are in demand. Personally, i've considered becoming a long-haul trucker myself, as it's a job in my area that's in high demand and has good job stability.
If you're willing to go back to school for a while, the trades (plumber, carpenter etc.) also become a viable option. Tradesfolk are in great demand, especially in many Western countries, and do offer a good pay - even for entry-level.
Do I find another traineeship to start over with?
Short-term trainneships and internships are worth considering, as they are a good way of opening the door to a full job. Give the company the option if you want to, to intern for a month or two.
Do I further expand my skills and learn different languages?
You should. Java is a good option to start off with, however the language has little in the way of flexibility. Java can be used for apps - but only for apps.
The more niches you can fill out with programming skills, the better off you are. I would recommend you to go further with something like C# - The language is popular and paves a direct road to ASP.NET. With ASP.NET, you can tailor complex webpages and APIs.
This is where the programming market is - if you can make webpages, webstores etc apart from isolated apps, you'll be much better off in the software dev world.
Or do I stick to what I know and dive deeper into that, getting more certifications?
In IT jobs, you have to keep moving - sticking to your comfort zone won't help.
Certifications won't do as much in the software world as it will in the hardware-related jobs. Focus on expanding your skills in more flexible languages, learn useful stuff like SQL and database design, and make sure you have something to show for it (ie. personal projects)
Do you think there are options to get (unpaid) work experience, even remote?
There are a good deal of options, including remote work. You could try doing some freelance through places like upwork or fiverr. It won't just give you work experience and things to show off, but also a bit of money.
Or have I just not found the right company yet?
As I said, there are a million ways to do programming and companies have just as many differing demands. Finding the right company in any IT-related field is much like finding the right girlfriend/boyfriend.
Seeing that you can program and that you are interested in expanding those skills, freelancing might be a good fit for you. You can make money off of it (with a bit of patience), and it allows you to create your own work/life balance. There are loads of opportunities that can also help you towards further projects of your own.
Fellow user Geoffery Brent mentions Specialisterne in his post - they not only help autists find work, but may also have a position for you internally. If you're in the US, Aspiritech might also be a valid option, though they don't hire remote employees currently.
As mentioned, there might also be similar opportunities in your part of the world.