Why Alpine? If the image is based on Ubuntu, than it is Ubuntu. Doesn’t matter what Linux distribution you are using outside the container if by “Alpine” you meant the operating system in the VM of Docker Desktop.
How? Please, share some details about what you are trying to do that fails.
I don’t see why that would be relevant. As long as your user is root, you can access it from inside the container, but sqlite is not designed to access it over network. If you need that, you need to find alternatives
Since Sqlite itself can only be accessed locally, I don’t think you will find many docker images for that. If you need it in a container, you can install it in your own image based on whatever OS you like