Very Unique Opportunity but not sure how to approach?

I am currently in a S&T role at a very small niche firm that pays very similarly to any typical S&T position - think the basic 85K + bonus or like $38-45 hourly for interns. The thing is we have a very small class and we're an expanding firm. All interns basically have verbal full-time offers for the position of our choice but I'm wondering if there will be an opportunity to work part-time in the Fall and if that's contingent on accepting our full-time offers...? I will be applying to other trading firms as well and am in the final round of some graduate 2022 positions. I absolutely love the company I am at now and don't want to burn bridges but I feel like this would definitely burn bridges if I had a full time offer, asked for a part-time position, and then declined them to work at another trading firm.

Now that I type this I realize this is absolutely ridiculous and disrespectful to my current firm, but in looking out for myself and personal growth/opportunities, are there any instances you all have "led a firm on" only to reneg and end up in a better position at another firm? I have gotten my foot in the door with this firm and come from an incredibly non-traditional finance background. I love the culture and the work I do here, but I'm always going to be thinking about the more small prop-shop culture with tons of talent, very developed technology, and name brand. The culture here is definitely more start-up with less developed technology but everything is expanding and growing so rapidly. I know I haven't even gotten the offer or started full-time as an analyst, but how did you all end up choosing your position to benefit your long-term career goals while balancing out the relationships and networks you've made at prior internships and companies? One of the only things I can think of that would not be as disrespectful and a slap in the face is to directly ask for more time to accept my offer, apply to these other firms, and if I truly want to work where I'm at right now leverage the competing offers for a better total-comp. With the position I'm in right now I think I have a delicate opportunity to have my cake and eat it too but it really depends on how I manage it and I'm unsure how to do so. Thank you for any help!

Tldr:

1) Verbal Full-Time, is there opportunity for part-time work in the Fall?

2) How do I leverage offers from other firms into a total-comp/title negotiation with current firm's full time offer

3) How did you all balance choosing your jobs for career development with respect for your current network and connections made at your prior internships and jobs

4) How much did you value culture and growth over total-comp?