As a second year CS interested in qualifying for internships and am interested in data science and ML, should I focus in them now, or competitive programming and discrete math, or algorithms MOOCs, or do projects?

As you are in second year I will say that try to maintain a balance between both projects and competitive programming.

Let me tell you some of my rejections stories.

During the end of the first semester of my second year, I heard from seniors about the importance of data structures and algorithms to get an internship.
I began to focus on data structures and algorithms. Solved many problems in DSA. I have done very few machine learning projects till that summer.
As summer vacations approached, I began applying for internships at various startups. Several startups rejected me because I didn't have good projects to show.
Few startups told me have a telephonic round and they started asking me questions on machine learning concepts.
I failed completely in each telephonic round. Also, I couldn't complete any assignments. At that time my skills were solving problems in Data structure and algorithms. I did not get internships.
Now, during the summer holidays, I started focusing only on projects related to machine learning and android. I didn't practise any questions on DSA and just did projects.
Now, after the summer holidays, Microsoft came to my campus to look for interns. I didn't have enough practice in the DSA questions and, therefore, I couldn't even clear the screening round.

I also applied for an internship at a mid-level company and also failed due to lack of practice on data structure and algorithms.

Now an important message: always keep a balance between your project work and problem solving skills.

You never know which company will ask what in the long term.

Edit 1: Thanks for all the love and support to this answer.

Tips for self-taught programmers and software developers