Here are some basic JavaScript data structures and algorithms (DSA) questions to help you get started:

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1. Array Manipulation:

• Write a function to reverse an array in place.
• Implement a function to find the maximum and minimum elements in an array.
• Write a function to remove duplicates from an array.

2. String Manipulation:

• Implement a function to reverse a string.
• Write a function to check if a given string is a palindrome
• Create a function to count the number of vowels in a string.

3. Searching and Sorting:

• Implement a binary search algorithm to find an element in a sorted array.
• Write a function to sort an array using the bubble sort algorithm.
• Implement the merge sort algorithm to sort an array.

4. Linked Lists:

• Create a singly linked list and implement functions to add, delete, and search for elements.
• Write a function to reverse a singly linked list.
• Implement a function to detect if a linked list has a cycle.

5. Stacks and Queues:

• Create a stack data structure and implement push, pop, and peek operations.
• Implement a queue data structure and support enqueue and dequeue operations.
• Use stacks to check if parentheses in a string are balanced.

6. Hash Tables:

• Implement a hash table data structure with methods for insertion, retrieval, and deletion.
• Solve the problem of finding the first non-repeating character in a string using a hash table.

7. Recursion:

• Write a recursive function to calculate the factorial of a number.
• Implement a recursive function to compute the nth Fibonacci number.
• Solve the Tower of Hanoi problem using recursion.

8. Trees:

• Create a binary search tree and implement functions for insertion, deletion, and searching.
• Write a function to perform an in-order traversal of a binary tree.
• Implement depth-first and breadth-first search algorithms for a binary tree.

9. Graphs:

• Create an adjacency list representation of a graph and implement functions for adding vertices and edges.
• Write a depth-first search (DFS) algorithm for a graph.
• Implement a breadth-first search (BFS) algorithm for a graph.

10. Dynamic Programming:

• Solve the Fibonacci sequence problem using dynamic programming.
• Implement a function to find the longest common subsequence of two strings.
• Solve the knapsack problem using dynamic programming.

These questions cover a range of basic DSA concepts and are a good starting point for practicing your JavaScript skills. As you become more comfortable with these, you can move on to more advanced DSA problems and concepts.