When/how do you actually bring in a structural engineer on a BRRRR deal?

Looking at a 3BR in Cleveland (44105/44125 area) — sub-$100K, CMHA Section 8 tenant target, DSCR refi down the road. On paper the ARV looks solid and there's real meat on the bone for a rehab.

But walking it, a few things gave me pause:

• Visible level changes room to room, floor-to-wall gaps in a couple spots
• From outside, the house reads like it's tilting slightly inward
• Porch has an obvious lean
• One section of the basement foundation was covered up, couldn't fully inspect it
• Exterior doors have daylight gaps around them (could just be old doors, could be the house shifting)

Nothing about it feels unsafe to walk through, and the walls/roof/panel/water heater are all in decent-to-good shape otherwise. But I'm not qualified to tell the difference between "100-year-old Cleveland house settling" and "foundation problem that eats my whole rehab budget." That's exactly the kind of thing I don't want to guess on.

So — for those of you who've actually done this:

1. Who do I call first? Structural engineer (PE-stamped) vs. a foundation repair company? I keep seeing that foundation repair outfits will do a "free inspection" but obviously they're incentivized to find (and sell) a fix. Is it worth paying for an independent PE opinion first, even if it costs more?
2. Timing — do you get this done during your due diligence/inspection contingency before you're locked into the deal, or do you close and immediately loop them in during the rehab-planning phase? Assuming I want an out if it's bad news.
3. Cost/scope — roughly what does a basic structural assessment run for a single-family in this price range, and what should I actually be asking for? A verbal walkthrough opinion, or a written report? Does a written report matter for anything beyond my own peace of mind — insurance, lender, resale?
4. DSCR lenders — has anyone had a lender request or require a structural report as part of underwriting, or is that more of a conventional-loan thing?
5. Negotiating leverage — if the engineer comes back with "needs work but not a tear-down," how have you used that report to renegotiate price rather than just walking?

Appreciate any real talk on this — trying to make sure I'm building good habits early rather than learning this lesson the expensive way.