I need some early career advice

Firstly, here are some relevant facts about me:

• I'm currently in my final year of a degree in real estate (and related topics) at a reasonably high ranking college (not in the US). This experience has strengthened my passion for subjects ranging from RE investment to urban design and place making, but I don't see myself applying for a masters over the next two years. 
• I was born and raised outside of the US, but I'm fortunate enough to have US citizenship.
• I've absolutely loved working in real estate during my previous internships (9 months + experience covering various facets of acquisitions and asset management). It would be fantastic to land a full-time job in the US.
• I have only really spent time in the US in NYC. While I'm very open to living in any reasonably sized city, I'm leaning towards NY because I don't necessarily have chance to get to know other places in the US before I get a job. 
• I have accepted an internship at a developer in the US (not in NY) which will commence in a couple of months and finish by August. It doesn't appear that the firm is actively looking for anybody to start full-time shortly after this internship finishes. 

I would be greatly appreciative of any response regarding the following:  

1. I've recently been targeting my networking efforts with people working in acquisitions or development in NYC. Usually, I look for analysts or associates at companies I'm interested in on LinkedIn. I then reach out with a pretty general message when I send an invite, stating that I'm going to be looking for a job and would appreciate a call for advice etc. Is email a better means of reaching out to people and is it advisable to reach out to those at levels higher than associate?
2. I was thinking of reaching out to companies in order to arrange an internships in NY to commence shortly after my upcoming  internship (ideally within acquisitions, development or investment sales/capital markets). I know this would be a second internship after graduating, but I guess it would give me an opportunity to go to NY, build my network/market knowledge and potentially land a job. I've not been too active with applications for full time roles recently due to a feeling that online apps without having built a bit of a relationship internally is probably a shot in the dark. I'm also going to have to focus on college exams over tonnes of prep for any superdays etc over the next month. Is this grad internship approach sensible given the context? If so, would a combo of a) networking and b) more directly sending my resume to companies be the way to go about it?
3. Any other advice would be greatly appreciated. While I understand this isn't LinkedIn, if anybody is willing to have a chat or is aware of a potential internship at their firm from August onward I would be hugely grateful. 

Thank you! I hope you have a great morning/afternoon/evening.