Yep, that is roughly what I meant on the chimney – wouldn’t bother with that on the stucco, it looks pretty smooth already so just term bar should be fine. I’d probably put the top of the plywood near to even with the next mortar joint up, then cut a kerf into that with a diamond blade so your counterflashing can line up with the top of the plywood.
Re: loose laid, there are a few different ways to secure the membrane to the roof. If I were doing this I would strongly prefer “adhered”, which amounts to glueing the membrane to the roof deck with contact cement. I think you said you want to do this in one piece though, which would mix poorly with a first time installer. There is a definite knack to working with contact cement, and it’s not something I can really talk you through.
“Loose laid” would be a ballasted application – more or less you lay out the membrane, seal any seams/corners, then put large smooth rocks (or concrete pavers) on the membrane to hold it down. I would see problems here as any movement in the system could cause the membrane to rub up against the deck, causing wear/leaks at any rough or sharp spot. (which will be hard to completely eliminate with OSB)
“Mechanically fastened” could work OK here – you still need to make friends with your local roofing supplier, as you need some semi-special screws & metal battens. Basically you screw a bunch of holes in your nice new roof, then cover them with seam tape. I don’t have much experience with this one, but it’s cheap and easy.
If I were doing this roof I would go over that deck with 1" isocyanurate board (or other flat roofing product) fastened with manufacturer approved screws & plates, then adhere the membrane to that & cover any outside corners with uncured flashing tape. I have most of these things in my shed though, so the expense might start to add up on you.
For you I would try pretty hard to afford going over the deck with a proper recovery board of some kind; if not, then get super anal about anything that looks sharp or rough on the roof, then either mechanically fasten or adhere.
If you choose to adhere, I would suggest that you go with ten foot strips of EPDM, and have a few seams. (Sealed with double sided tape). This will be plenty frustrating enough for a beginner to glue down, without trying to handle a single large piece.
How big is this roof anyhow?
I’m happy to walk you through this as much as possible, but I do suggest you get friendly with the guys at some place local to you like ABC Supply. They (probably) won’t be roofers, but they will know what roofers buy and should be able to help you out with what is locally available. These systems differ quite a bit depending on the manufacturer; I’m mostly familiar with Firestone.
Glad to be of help,