So I would have had to form an LLC on a property prior to placing my offer.  

However, because that house was renting to 5 people prior (legally), they would still be allowed to continue that use.

I'm in New Hampshire.My net worth is pretty good because I own this and another STR condo outright but I'm low on cash flow due to prior rehab and just coming out of the slow season.

I document with pictures, give the tenant instructions on how to pay me, and hold the property for XX days (check state law).

The IRS is only looking for a copy of the relinquished property sale contract, they don't necessarily need the contract for replacement property right away as the FIRPTA exemption needs to be approved prior to the closing on the sale of relinquished property. 

(Prior to graduating college and getting a full time job, I was an incredibly social person, so this was a huge change of mindset to sacrifice the way I did).And on the other end, my brother decided to start his own business while I was working and did not work hard as he spent money like crazy and eventually went bankrupt (filed 1 year ago) .

If by partnership you mean a legal partnership (LLC or LP or otherwise), then that legal entity would need to either dissolve (or deed out your 50% to you) prior to sale before you could sell your own 50%. 

As long as you sell it while you have still lived in it for two out of the 5 years prior to selling it you can still take the $500K tax free. 

Any damage to the wallpaper, paint, walls, floors, carpeting, doors, windows, window treatments, light fixtures, appliances, or other improvements to the Property (to include burst water pipes due to freezing caused by neglect or carelessness of the Tenant, his family, or any of his guests), in excess of ordinary wear and tear, shall be promptly repaired or replaced by tenant, at Tenant’s sole expense, so as to restore the Property to the same condition as existed prior to the commencement of the Term.

I’ve heard from some lenders that I need more equity, others said there was a “cooling period” required after purchase to be able to use additional gained equity in land (from rezoning), and others needed prior experience.