FT recruiting for an undergrad junior?

I'm an undergraduate junior with an upcoming summer analyst internship at an EB (close a MM tbh tho) in their TMT group. I like the people in the office and can see myself doing FT there, but there's a part of me that also wants to try for something "better" (i.e. i guess higher paying, a better name bank that will set me up more ideally for PE recruiting, I might also apply to some FT PE positions as well). Stats are that I go to a non-target, Stem Major, 3.6 CUM GPA, 4.0 Major GPA, eh Extracurriculars, but I feel I come off decently during interviews. Obviously have to sort out technical interview aspects since it has been a while.

Given the current economic conditions and how FT has gone down over the past few years, I've got a couple of questions.

1) General advice for FT recruiting?
2) When should I start reaching out for networking calls for FT recruiting?
3) Any banks that I can count on that will probably have open FT spots?
4) When would I have to wait until to know that FT apps are open?
5) Guess the most important question - will I look like a dickhead for trying to recruit for other banks FT while not having even completed my SA internship? Obviously won't be a dickhead otherwise, but idk if there's a stigma against doing FT networking calls even before doing an internship. Also, should I mention that I do have an upcoming summer internship at my current bank in the email or does it not matter that much? Thinking it will help bc it shows I have actually secured an offer and am a little more polished resume wise than otherwise.

Any pointers would be of great help, thank you!