CS Student Interested In Trading - How to Prepare for Next Recruiting Season?

I've been browsing around this site for a while and its about time I reach out for some suggestions.

I am an undergrad sophomore in CS at a top 5 CS school with a 3.9+ GPA. I have secured a software engineering internship at a prop trading firm/quant fund, although I've had a growing interest in trading since then and next recruiting season I wish to secure a trading internship at a proprietary trading firm or hedge fund.

I was wondering what other things I could do (at my internship and outside of work/school) to improve my prospects for an internship next year. I already am involved in trading competitions and one related club, are there any other recommendations?
--What types software projects at my internship would be most helpful in giving me skills relevant to being a trader?
--I have no experience trading my own portfolio, would this be a worthwhile activity to start?
--I am working on building my own algorithmic trading platform and simulator for educational/extracurricular use. Should I focus more time on non-programming activities or will this be looked upon favorably at quant-heavy trading firms and hedge funds like Jane Street, Jump, Citadel, etc.
--Do these top firms hire trading interns without experience? Or I should I focus on lower-tier firms?