What is the condition of the home and trailers? 

Well, most of the time (maybe all of the time) you're buying HUD houses "as-is" and you're not really using the presumed condition of the plumbing as a bargaining chip.

Or not keeping the property in a livable condition.

Should I close, if yes with what conditions ?

One approach could be to let her know you will let her use the last month's rent as her deposit if she makes sure the house is in good condition and clean when she moves out. 

@Khayla WilliamsI strongly recommend against borrowing 100% for a propertyThere is significant risk in owning real estate including section 8 and maintaining the home in a certain condition and if you do t have the funds for those repairs you could lose it all.I always recommend people budget and save enough for a down payment and reserves before getting into their first property.

However, a quick glance at Zillow reveals some new or decent condition rental listings lingering for over 30 days.

You must use numbers that are representative of the property’s condition if you are not going to renovate it before putting it in service.

Are there addition conditions I should consider if I do lease to them?

I've focused my attention in the area between Hwy 44 and Gravois Ave from Tower Grove Park down to River Des Peres for a nice intersection of price and condition.