I joined the Twitch Affiliate Program today and I also know that I have to register a business.
If I already accept donations and subscribers, do I have to register a business directly or can I take my time there and do it in 2-4 weeks, for example?
The earlier the better
Legally, now that you already have a profit intention. Commercial law does not set any sales or profit limits from which you have to register a trade - just the intention to make a profit is decisive.
In practice, however, many trade offices are accommodating for a few days or weeks and you can then register the trade retrospectively. However, they are not obliged to do so - theoretically, they can also impose a fine on you. You can also kindly ask the respective office how they handle it.
What if I don't have the funds for registering the trade yet but only in the 1st month? Does this mean that I should only start streaming again after I have registered the business?
You can also stream without a trade. But if you want to make money with it, you can only do it with business. If the money for the business registration is not available, that is not the problem of the trade office - and as I said, there's still the possibility of retrospective registration, but I would clarify this with the trade office.