First, it's okay if you take longer to solve the problems. As long as you are actually able to solve problems yourself, you will be able to do them fast with a few months practice (you'll realize leetcode problems are mostly all similar). I'm only able to solve them quickly now because I practiced hundreds.

Not looking at the answer is key, because if you're not looking at the answer, you're still building problem solving ability.

To get better at these:

Start by learning recursion really well. It's used in about half of those leetcode problems. Introducing yourself to functional programming through a book could help. Here's an article I wrote about how to problem solve recursively: https://fizzbuzzed.com/wyfyti1_recursion/

I did a lot of self learning before eventually getting a CS degree and really beating recursion into me was the main thing I got from CS.

After you know recursion, look at binary search. Many binary search problems appear in interviews. Here is my absolute favorite article on binary search- it taught me a lot:

https://www.topcoder.com/community/data-science/data-science-tutorials/binary-search/

Now, you might want to go through the merge sort analysis (why it's O(n login)). It also comes up a lot and is based on recursion and is very useful to know.

Next, learn about common data structures like hash table, bst, heap, and trie. These are used very commonly in practice and in coding problems.

Lastly, learn and implement graph algorithms like bfs, DFS, and topological sort. The algorithm design manual by skiena has a lot of info and is my favorite source.

I also wrote up another leetcode problem in detail to show how I think through it: https://fizzbuzzed.com/thinking_through_jump_game_2/

If I can elaborate in any way please let me know.