Hey! Full disclosure I’m more a “marketing designer/developer” than a frontend engineer. I’ll try address your post point by point to start 
Is Webflow going to let me export our code and handing to my senior frontend engineer without him hating his life?
Yes and no. You can export the code, but keeping everything on Webflow hosting is much easier for CMS (collections). There are a few work arounds but most of my clients I recommend using Webflows own hosting! I export my static sites and host them externally, but anything with a CMS I stick with Webflow’s hosting. The one thing I ask is why are you needing to hand the code to your senior frontend engineer? If you’re building a web app, then Webflow is not for you, unless you are looking at using Wized with Webflow!
Is Webflow going to name variables well and keep our code organized and easy for humans to read and work with?
It’s up to you to name your variables in a way that makes sense! Webflow doesn’t do this for you, as it’s very much a “visual HTML/CSS code editor”. I recommend checking out Client-First Style System for Webflow by Finsweet as this is becoming “industry standard” for Webflow.
The code that Webflow exports is actually easy to read so thats a bonus! It’s up to you to ensure the classes all make sense using whatever structure you want.
Am I going to be able to fetch data from our backend and combine a more “normal” data flow with whatever Webflow is doing?
Yes, although you’ll want to look at using something like Zapier. Webflow also allows custom code so if you know what you are doing you can do “anything”. Again it depends on what you are doing, if you are building a Web app then I’d again, recommend against webflow. (Although they do have dev lnk which is a tool I haven’t looked at DevLink – Visually design and build web components for React | Webflow)
Are the webflow APIs going to have some some bug deep in some proprietary code that creates a nightmare for my team?
Honestly I don’t know! I’ve never used the Webflow API, I’m a designer/Webflow dev and run more on the marketing side of things.
Some of the complaints I’ve heard about webflow are actually that it’s “too hard”, which is a terrible argument. One video actually complained that “in order to be truly efficient in webflow you have to actually understand the fundamentals of web development”.
I agree with this! A lot of “squarespace”/“wix” users think Webflow will be similar, but it is truly in essence a visual code editor. You need to know what html/css/some JS to know what you are doing, but if you know that I think it’s a truly marvelous tool!
Again I come from a more marketing side of things, I’ve never built web apps, but I have applied business logic to websites using things like Zapier to do “if this then that” style responses! I think Webflow is great, however depending on the use case you may either want to look at Bubble, Wized/Webflow combo, or some other platform if you are actually building an app. As Webflow is best for brochure sites not full scale applications.
Webflow wants you to host on their platform and their CMS/editor capabilities are excellent for handing off to clients and allowing them access to only whats needed!
Hope this might provide some insight! If you have any other questions feel free to reach out.