Your questions could do with more focus
It's a hard question to answer. Generally homebrew is most balanced when it is most similar to existing content. There are certainly a lot of situational and niche content which is balanced. With regards to complexity, there are some complex class features, most tend to be 1 or 2 sentences but there are some with as many as 5 sentences. Homebrew already adds complexity since it is new too.
Your title and 3 questions asked within are all difficult and broad:
- Does PC-tailored homebrew require special considerations? This is a hard question to answer objectively.
- Is making a functionality (replacement class feature, new feat, a spell) with complex requirements a bad design? Bad in what way? You probably shouldn't make something more complex than the most complex feature, but why not, there's nothing wrong with it.
- What about feature synergising with other optional ones? What are you asking? General thoughts?
- How to ensure an option filling very specific gap is balanced across different play-styles? Which play styles are you talking about? There are play styles where balance doesn't even exist, let alone adherence to rules.
This question is very broad, and I'm not sure how you will measure a good answer. For example if you ask "are complex requirements bad design?" how can I answer? What does "bad" mean? How complex are we talking? Even if you answer those, how can we discern a good answer from a bad answer?
I understand that you are asking about balance, and making niche features still useful for different playstyles. Beyond that, there are a lot of very broad and vague questions that are so hard to answer!
I think you should consider your goal and ask a more direct question, I think your goal is something like: "I want to make content that is niche, but still useful and balanced." As for the question, I'm not sure exactly, it seems to be "how do I do that?"