In Anna, actually, by the Tachanun part, which we discussed on Friday, the exact setting of how we sit is how we put the head by the arm. Now, is sitting a requirement? There are two different angles. The Rivash, a Rishon (early authority), says that the fact that we sit at the beginning of Tachanun is simply because you don't need to stand. There are parts of the Tefillah (prayer) that need to be said standing, like the Amidah. This is not one of them. You don't need to stand, and therefore we sit. In other words, according to him, it is not a requirement to sit. It's just a default option. The Beit Yosef brings that. But then he also brings that al pi Kabbalah (according to Kabbalah), the Mekubalim (Kabbalists) say that it's actually very significant and necessary to sit. It's not just the default. In fact, we sit by Tachanun on purpose. And then they add: What's the logic? The logic is simply that sitting is considered Hachna'ah. It's considered a degree of humility. And humility is necessary when you're talking about Tachanun, when you're talking and pleading for Hashem during Tachanun. So we do sit during that time.
However, when you find yourself in certain situations, let's say you can't sit. Someone behind you is in the middle of the Amidah, and you're backed up, but you can't sit down. Because halachah hi (that's the law): you should not sit down if someone's right behind you. Should you say Tachanun standing? You should say it standing.
Or another instance: you're in one spot of Tachanun, and the Kahal (congregation) are all standing up because, let's say, it's a Monday or a Thursday, and they went ahead and they're all standing already by now, and you're about to sit. Should I sit, because you just said there are those who say it's necessary? You should, in that situation, do a little differently. What you should do is stand, because the Kahal are standing, but lean on something. Leaning on something is considered a combination. So you stand in that situation and lean on something to show a little sense of sitting. Each situation is different. Again, ultimately, normally we sit. Typically, we sit. When there's a situation where you can't sit at all, you stand, and it's fine. When there's a situation where you shouldn't sit because the Kahal are standing, you stand and lean. Those are the halachot (laws). Have a great day, Kol Tuv.