I am planning to graduate early from college (in three years), what should I do with internship recruiting?

By way of background, my plan is to study math along with either philosophy or EALAC at a target school (maybe semi-target? It's not one of HYPSM or Wharton but pretty much right after them. My school does not have an undergraduate business school, so recruiters are typically chill with majors). I took a gap year for 20-21, so I will enroll in fall 21 as a freshman. During the gap year, I've been doing internships at several PE investment shops and am set to intern at a family office that invests in hedge funds. My hope is that I could break into a hedge fund right after college.

Summer 22, technically, will be my freshman summer but I'm also planning to graduate in 3 years with AP credits from high school and all. If my plan to graduate early goes through, I will only have one summer left after summer 22, so it's probably necessary for me to seek out some legit summer 22 opportunities (basically like other sophomores). In this case, here are a couple of questions:

1. Should I say that my expected graduation year is 2024 even though it should normally be 2025?

2. What should I do with my transcript which will not even have my first semester's grades up by the time a typical IB recruiting season ends?

3. Are there any firms that you are aware of that will consider situations like my case seriously? (I'm mainly looking at banking/hedge funds/quant shops)

4. If applications to big names don't fall through (which is very likely), what other options are there so that I could build up to securing a desired junior summer internship in 2023? (Most diversity programs don't apply to me, but feel free to drop them in case they may be helpful for other people in my shoes)

Thanks a lot. And you responses are appreciated by everyone who plans to graduate one year early (many people do this to save tuition costs) yet hope to break into the finance industry which is having this increasingly squeezed timelines.