Help/Tips for MMs and Boutiques?

Hello everyone,

This is my first post here. Thank you very much for reading in advance. If you are pressed for time, please skip to the end questions.

I have always been a lurker, but given recent events I've made an account to post. I'm a junior, 3.9/4.0 GPA, economics major, with previous finance experience in corporate finance and risk analysis, and I want to go into IB.

Only 4 BBs recruit directly from my school, and I networked at both firm events and through my school's alumni network for months (not an athlete, member of a frat, etc. so had to build my own network) and landed 3 interviews. Got guides, practiced, studied, etc.; made it to superday - but no offer. There's one BB left - where I was fortunate enough to network with an alumni who was in charge of the first-round selection process and promised me first rounds - but I'm becoming very aware of the need to apply elsewhere.

Fortunately, one of my Superday interviewers at the last BB I interviewed with talked with me on the phone afterwards, giving solid feedback and saying to feel free to contact him for mock interviews and any other help I may need. His helpfulness and optimism helped with the disappointment a bit.

Anyways, now I am definitely applying everywhere, and plan to reach out via email to boutiques and MMs within a week. My university alumni network doesn't have anyone at any such firms. I know this is not a time to give up - some days you're the dog, and some days you're the hydrant. I still want to push for banking and am exploring my options.

I share a short version of my story in case (a) anyone out there, lurker or otherwise, is in a similar position and is curious, and (b) to show that I am willing to share my story, hopefully making people comfortable enough to share theirs.

My (more concise) questions here are for anyone and everyone willing to answer:

1. Is "cold-emailing" the best way to network with MMs and boutiques? (I don't have any connections, e.g. alumni, there.)

2. Is it considered "wrong" to take the initiative and keep in touch with the networking contacts I made during the process (where I didn't get an offer)? A few emailed me on their own to talk and stay in touch; I'm not sure if it would be improper etiquette or offensive to try to keep in touch with others who didn't email me on their own.

3. If you went through this stage, how did you make it through?

As you may be able to tell, I am new at this but tried my best to do my research to get into the industry. I am still learning about how the whole recruiting process works.

Thanks so much in advance to anyone who reads/answers. If anyone would be willing to discuss this further, I'm definitely down for PMs, emails, and so forth. All I can offer are bananas and gratitude.