“Steadfast” suggests permanency or constant loyalty, such as in your example of a steadfast friend or steadfast supporter. The word is often used to describe things, not just persons: “My friends always give me their steadfast support.” “I can’t speak Russian despite my steadfast attempts to learn it.” “Steadfast” emphasizes that something continues over an appreciable amount of time. “Adamant” emphasizes a person’s unwillingness to change his ideas, opinions, etc. The word does not suggest that the unwillingness lasted over time. Example: “My friend asked to borrow my car. I could see that he was drunk, so I told him no. He asked me again, but I was adamant [very unwilling to change my mind], and I told him no again." “Unyielding” suggests that you are resisting pressure or influence from someone or something. That is, someone or something is trying to make you do/believe/think/etc. something, but you will not submit. Example: “No matter how many times they told him he should stop what he was doing, he was unyielding in his determination to finish." “Stable” means resistant to change; unlikely to change position. “Stable” is often used of inanimate articles, like in your example of a “stable ladder”. "Stable ladder" sounds unnatural and wrong. Here's a place you can find collocations galore: http://corpus.byu.edu/coca/x.asp?r1=&w=1280&h=720

"Steadfast" is suggests personal loyalty, or loyalty to duty. It's only used with people--or, anthropomorphically. Hans Christian Andersen wrote a story entitled "The Steadfast Tin Soldier." It's positive and complimentary. I'd be pleased if my wife called me her "steadfast companion." "Adamant" and "diamond," the hardest substance on earth, come from the same root. "Adamant" means hard, completely unyielding. It, too, is used mostly of people. "I tried to convince him to yield on this point, but he remained adamant." It's rather uncomplimentary--it is similar to "stubborn." It applies to opinions or choices, not directly to people. You can say "he was a steadfast friend" but you can't say "he was an adamant enemy." You could, however, say "he was an adamant Republican, and would never vote for a Democrat under any circumstances." "Unyielding" can apply to anything--human, animal, vegetable, mineral--that is hard and won't yield. "Unyielding" means something that doesn't move even when you push it. "Stable" just means something that stays put under normal circumstances, but might well move if you push it. Something can be stable, yet yield to force. For example, a broomstick balanced on your chin is unstable--it falls over if you don't keep dancing around under it. As you say, a ladder is stable. You can walk away from it and it won't fall over by itself. But it will fall over in a high wind. A lighthouse is not only stable, but unyielding--it can withstand a heavy storm.