If you dont rent out that 3rd unit and will stay in that unit till you purchase the new property then you will need sufficient income to qualify for the full mortgage (PITIA) of the new property with the net rental calculation of the current triplex using only 2 units (since youre living in unit 3) which may result in a much less favorable rental calculation than you had previously planned for.

Normally for that i see ppl verify applicants should have sufficient funds equal to 3 months of rent in that case?

I would assume any court actions, along with an LP filed, sufficiently cloud the title, so the seller can’t reasonably give clear title.  

However my real concern is you mentioned that your bills depend on their ability to pay as well which implies that you don't have sufficient cash reserves to handle financial hiccups without putting yourself and your family in a financial tight spot. 

But I'd want a sufficient discount that it was worth it.

They just include a few requirements such as the borrower having enough equity in the property, sufficient cash on hand for making monthly payments, and a reasonable strategy to exit.

In most cases, a new coat of paint - or at the very least, repainting areas that are presently chipping, is sufficient.

A $200 fine is not sufficient if there's been a significant amount of smoking.

It's really going to be hard to provide any realistic feedback without knowing the size of the property, the quantities of work and more details on the specific repairs and location of the project.How many square feet is the property? 

I'm also not able to qualify for FHA because properties in my market do not meet the self-sufficiency rules.