This is a longish answer that goes off on a lot of potentially unrelated tangential points but please stick with me here if only because it's interesting!
I'm paraphrasing an answer from here for this first bit. Basically in ancient Japan there were only four colors in wide use, namely 「あかし」「あおし」「しろし（しるし）」「くろし（くらし）」. From these you can naturally see how they became the four pure adjectives that we have today, 赤い, 青い, 白い, 黒い. Other color words were gradually introduced over time, but 黄色 alone is special in that there were never really any references to "yellow" in really old texts. The kanji 黄 was used in some words but none that explicitly referred to yellow. It's possible that they just included "yellow" under another color's name. It's not until the 10th century that you see the word きいろ in use, and the only explanation given is that it's "the color's name plus the 色 kanji."
This site offers some explanations as to where the term itself came from but there doesn't appear to be any solid evidence. Examples include various types of trees as the root for き or perhaps a transition from some other words beginning with く, like from くがね or possibly くそ. It's possible that since 黄色 came relatively late compared to other colors like 茶色 they just continued the pattern of adding 色. Or maybe it was just too confusing just saying き. It was originally 黄の色 and shortened to 黄色.
At any rate this explains why you have this weird yellow situation.
Now to answer your real question, in most situations I can think of you would need to use 黄色 and not just き, at least in normal speech. I can find a few examples on alc of 黄 by itself, as in 黄がかった or 黄なる.
The issue with things like 黄河 is not that they are proper nouns but that they are words of Chinese origin. 黄 is not a concept of Japanese origin, and there are plenty of Chinese words that use it. You'll just be using it with 音読み instead. Like 緑黄色野菜 or 黄変 or 黄斑 to steal a few from alc.
All said, there may very well be instances of 黄 outside of words of Chinese origin that don't have 色 after them. But for pretty much any modern purpose you will always be using the word 黄色. That's just The Way It's Done Now. I haven't looked up the origins of murasaki yet but I'm sure that has its own unique story and use patterns as well. For now you might just be better thinking of it in the same category as 茶色.