Already posted on another subreddit, sorry if that's frowned upon but I don't use Reddit often and I'm eager for some feedback. My apologies if some of these questions seem stupid, I have very little knowledge of getting internships in general, let alone very competitive ones.

For context, I am currently attending community college in California and have guaranteed admission to UCLA, Berkeley, and UCSD. I have a 3.6 GPA, no academic achievements other than dean's list all four semesters at CC, and I'm an applied math major. Only one internship that wouldn't be notable to any big tech or quant company. I'm super motivated, I'm a good self-teacher, and quant finance is my number one choice for potential careers at this point in my life. The role that seems the most appealing to me is trading but I'm open to anything I'm competitive for at the top firms

1.) Are the highest echelons of quant finance, (Jane Street, Optiver, HRT, Jump, etc.) so ultra-competitive that I don't even stand a chance having gone to CC? Am I screwed right from the app screening phase just by virtue of having gone to CC even though I will finish my last two years of uni at a great school?

2.) Given my university options will be all California schools, is Berkeley my only choice to be truly competitive in these interviews? I haven't seen anybody on here nor YouTube talk about how they got into quant finance from anywhere other than Berkeley (as far as California colleges go).

3.) Is being really good at coding an absolute must? I have seen some people say that depending on the role you apply for you, won't get any coding questions in your technical interviews. I've also heard others say that no matter what you have to be pretty talented to even have a chance, completely irrespective of the role you're applying for. Are there good roles that only require proficiency as opposed to absolute mastery?

4.) Can anybody speak from experience or share relevant anecdotes about people you know who have landed a good internship without being like a super special standout student? I have never competed in a math competition, I'm decent at coding but not amazing for my age (2nd year college), I have zero industry connections or relevant experience other than doing lots of math and coding in my free time,

For anybody who read this post and took the time to respond, I thank you very much. I am incredibly excited to try and pursue quant finance.