On the plumbing, did it say if the test held or failed?

I bid on a triplex property listed for $125,000 and my offer was not accepted. 

He should have run a prelim title report to identify junior lien holders, as tour your offer may have to be structured differently to deal with them, ie. lower purchase price as you may have to contribute additional cash to satisfy am junior lien.There’s too much to learn for You to know everything involved.The list price is irrelevant, the price the bank will eventually accept is what matters.Worst case, get a contract executed, provide a legit POF or preapproval, see where the bank comes back.

I know the likelihood of getting my offer accepted is better without contingencies but those two seem to be pretty important. 

You need an environmental testing company (or at least someone who knows more about it) to test the house.

We offered all cash with no inspections, which after a little back and forth was accepted.

If you’ve never done a deal I suggest presenting to possible private money what the deal will look like if your offer is accepted.

I don't want to get in a situation where I have an accepted offer and I can't get underwritten. 

PMs are not created equal and can pass/fail an initial sniff test by reviewing their website/social media platforms and the initial contact.Best of luck in your search for a new PM.

This was a verbal offer that I decided to just accept without a counter.