I'm not a pipx expert (I'm a "I got it to work for my use case and then stopped" person :) ) but I was able to get my project working after installing a local wheel file (so i don't think you need access to the Internet to install things).
I thought the wheel file has all the dependencies since (my understanding of) pipx uses a venv for each individual wheel file/app. Certainly I'm using a bunch of packages that I needed to pip install into my development environment, but it's entirely possible that my pipx-managed wheels are using those installs, too.
I think the last two points are accurate, and I've never tried to use APIs like wsgi with it.
If you have a shiv working it stays working, assuming you have a solution to distribute the required interpreter version.
- it doesn't provide a single file for a full project with all dependencies.
- it requires internet access on the target machine to install things.
- it can't give you access to underlying API for things like wsgi.
- it requires pipx on the target machine.
- it requires a wheels made from a build, which many projects don't have (such as a lot of web projects).