Yes, definitely. I was a programmer years ago and like to think I have a very logical, algorithmic mind, and a few of those set me on my heels.
Don’t worry about it, just learn. Everyone struggles with something. In the words of Will Rogers, “Everybody’s ignorant, just on different subjects.” Maybe you’ll be better at some other aspect of the job, like design or networking, two areas where I suck.
Just persevere. And learn.
Yes, where possible, always break it down into steps and test those steps. If you have the right idea about what those steps are, and you build and test them correctly, then when you put them together, it will work. But be patient. It takes a while. Eventually you’ll develop a sense for these things and how to approach them. You’ll develop a sense for how to plan them.
There are plenty of books and blogs and videos stepping though algorithms, I might take a look at some of those. After you finish an FCC algorithm, maybe check youtube and see if someone else solved it a different way. Understand their approach. Sometimes there is one best solution. Sometimes there are a few.
Just be patient and learn. If this were easy, then everyone would do it and it would pay minimum wage. The fact that it is difficult means good wages and job security. It’s a good thing.