There's a lot of bad information here on Berlin. For context, I'm a non-EU software developer that lives in Berlin and now has permanent residence, as is my girlfriend.
Germany is actually one of the easiest countries to get an immigrant work visa for. I would recommend skipping seeking asylum. There's a large enough job market in Berlin for developers that the work visa route will almost certainly be the fastest and least painful for you.
If you have a university degree, you should be able to get a Blue Card. In fact, Germany will give you a 6 month visa to visit the country and look for a job. Since you're already working remotely, finding money to support yourself during that time should not be difficult.
The salary requirement that others list here is incorrect for software developers. The typical Blue Card minimum required salary is €46,400/year, however, software development is an in-demand job ("Mangelberuf"), which lowers the minimum to €39,192/year, which is above the standard salary that you'd find for development positions at Berlin startups.
If you go the Blue Card route, you'll be eligible for permanent residence in 3 years.
If you don't have a university degree, you're still in pretty good shape. Then, in practice, what you need is a job offer (with a contract). Your residence permit, prior to getting permanent residence, will be connected to your specific job at a specific company (though in practice this just means you have to go to the foreigner's office to apply for a new visa when you change jobs). This was the old system that I went through (before the Blue Card was introduced, which my girlfriend used). Basically if you have a job offer and a reasonable salary, you're next to guaranteed to be able to get a work permit. I've never heard of a software developer having their request denied.
However, that system is not nearly as streamlined, so you actually usually need to already be in Berlin to apply for it. I would recommend finding any excuse you can to come to Berlin on a visitors' visa (language course, conference, whatever) and stay as long as you can. I think you'd be able to find a job and kick off the work permit stuff in a 2 month timeframe.
Going that route you're able to apply for permanent residence after 5 years, though it's a slightly nicer version of permanent residence than the one you get via the Blue Card route since it's transferable to all EU countries except the UK and Ireland.
Official things in Germany will naturally be mostly in German, but the startup scene functions primarily in English. It's totally normal for job interviews and work meetings / emails / etc. to be in English.
If you have questions on this stuff feel free to drop me a line. My email address is in my profile.