Develop Reference

How does Python come off as a multi-platform programming language?

I'm talking about deploying Python-made, GUI-based, desktop applications via .app and .exe format for OSX and Windows. As far as I've gone into Python, I've only seen it as an application that runs on the Terminal / Command Prompt. I know that it is possible to create a user interface for it using various offerings on the internet (wxPython?). I just want to see how it passess off as a way for a developer to create mac and windows applications with as little code difference as possible.

I find that Python is a very good language for GUI programming. As you have stated, you can use the bindings for wxWidgets (wxPython), but there's also a binding for just about every other cross-platform GUI toolkit you can think of (Tk, Qt, GTK, FLTK, etc.). These GUI toolkits should allow you to make a program that will run unmodified on most OSs.
In terms of Python OS compatibility, it will behave virtually the same on all OSs, except for one or two modules such as mmap.
Using py2exe, py2app, or similar tools, you can embed a Python interpreter (along with your program's bytecode and it's dependencies) within an executable, making it easy to distribute an application. An end user can then open the program as they are used to. If you want the "security" of a compiled language, Python will not be the best language for you to use (but I prefer readability over safety :).
Another thing to consider with cross-platformness is what OS specific features you plan on using. Most GUI toolkits will not support things such as Microsoft's DWM (though you can use OS features through ctypes).

I think what you're looking for is PyQT and Tkinter. Both are GUI Libraries for use with Python. Both are cross-platform. Further, for packaging up .exe and .app for distribution, look at py2exe and py2app.

For Windows, the easiest approach is py2exe. There's also a similar project for MacOS. It's called py2app. Most GUI frameworks are cross platform. Just check their documentation, or even the home pages should have it.
Make good use of the os module. It has many function that will handle cross platform situations. A common example is file paths. When you build a path should it be backslash or forward slash? os.path.join handles that for you, and works based on which operating system it's running on. You shouldn't have to modify your code at all when shipping from OS to OS. It should run on Linux just as well, naturally.
By the way, MacOS often comes prepackaged with Python. As long as it's a somewhat recent version this can make the difference between a Hello World script being 1kb and 30mb, so avoid packaging Python with it. Unfortunately Windows isn't as well equip. Consider an option for "I already have Python installed" when downloading the exe.

implement a database application with GUI for Windows, written with Linux

I have the following data scheme that I want to turn into an application. A regular desktop GUI would probably the best.
UML Diagram http://img217.imageshack.us/img217/341/56836587.jpg
big version
The whole thing would be developed on a Linux (Ubuntu, Gnome) machine, and then used on a Windows Vista computer. If Windows is a problem, I might be able to just run it in a Linux VM later.
My programming language of choice would be Python. I have only used Qt for a two hour project, I have pretty much no experience with GUI. Would Qt work easily on Windows and not look to out of place there? Is GTK a way better option, or is that merely preference issue?
From talking on the #python channel, I gathered that storing the data in a SQLite database would be a good option, and accessing this data via the SQLAlchemy ORM would be better than writing SQL statements by hand. The latter is my usual approach, I want to use this project to learn something better.
Can I just design the dialogues in Qt Designer and use them with my Python objects?

You might want to check out Dabo.
Dabo is a 3-tier, cross-platform application development framework, written in Python atop the wxPython GUI toolkit

Camelot

If you are set on using Python them I think Qt would be am excellent choice. It's a fantastic framework that looks good and runs on many platforms. You won't be limited to Windows. Qt can be a bit intimidating but you won't be limited in terms of functionality. The Qt designer works well with Python.
SQLAlchemy works on all common desktop platforms, including Windows.

How to export python functions and reuse them in another app

I was wondering if there is any way to export python functions to dll. There is py2exe and I can successfully create exe file. My program should be used by another program written in delphi (there is possibility of importing dll's in delphi).
So I was wondering what would be the best way to connect those 2 applications.
Now I can only create exe, execute process in delphi and communicate in some way. But I don't think that's nice way. Maybe somebody have any experience in this subject?

There are some pretty big challenges to making languages work well together. As a simple alternative to trying to hook python code directly into delphi, you could consider using something like an xmlrpc server to provide python functionality remotely.
http://docs.python.org/library/xmlrpclib.html
Of course, any protocol could be used; xmlrpc just has some useful server utilities in python and presumably has a client library in delphi.

You can re-use python functions via modules. Integrating with other language is a different task all together.
py2exe packs all dependent modules and additional dlls required by an application so that it can be easily distributed without creating any installation dependencies for the user.
Cross - language integration requires some work. To integrate with "C", there are various ways like cython etc. If there is similar facility available with delphi, you might be able to use it.
Check out some of these references, it will make it more clear to you on what direction to take.
http://wiki.python.org/moin/IntegratingPythonWithOtherLanguages
http://www.atug.com/andypatterns/pythonDelphiTalk.htm
http://www.google.com/search?aq=f&sourceid=chrome&ie=UTF-8&q=python+delphi (Google search)

What's a good embedded browser for a pygtk application?

I'm planning on using an embedded browser in my pygtk application and I'm debating between gtkmozembed and pywebkitgtk. Is there any compelling difference between the two? Are there any third options that I don't know about?
It should be noted that I won't be using this to access content on the web. I'm mainly using it for UI purposes.
My priorities are:
It needs to be stable.
It needs to be cross-platform.
It should be easy to use.
It should be actively maintained.
It should be extensible.
It should be fast.

gtkmozembed is not available on Windows, although you can use the gecko embedding interface directly. This would require you to write some C++ code.
As far as I know, the gtk webkit port is not available on Windows yet, and still appears to be undergoing a lot of change.
For an example of a cross-platform gecko embedding solution, check out Miro.
Miro is python, and they've written just a couple of C++ classes to embed gecko on Windows, while using gtkmozembed on linux.

if you judge by the web pages then definitely pywebkitgtk
pygtkmoz from this page
"Note: this project is no longer maintained. Please use gnome-python-extras (http://www.pygtk.org) instead. I apologize for any trouble this might cause, but this is better in the long run. Python bindings for GtkEmbedMozilla."
and pywebkitgtk looks like active project changes

How do I develop and create a self-contained PyGTK application bundle for MacOS, with native-looking widgets?

I have read that it is possible to build GTK+ on MacOS X. I know that it's possible to create a bundle of a GTK+ application on MacOS. I also know that it's possible to create widgets that look sort of native. However, searching around I am not really clear on how to create a bundle that includes the native theme stuff, and uses Python rather than its own C main-point. There are also rumors that it's possible to build PyGTK, but it sounds like there might still be some wrinkles in that process.
However, there is no step-by-step guide that explains how one can set up an environment where an application might be run from Python source, then built and deployed in an app bundle. How can I go about doing that?

Native looking widgets is quite complicated.
There's a beginning of quartz engine (for theming) found here http://git.gnome.org/browse/gtk+/tree/gdk/quartz
For self-contained applications check out the newly released bundle on http://live.gnome.org/GTK%2B/OSX

I'm not sure if I'm grokking all the details of your question, but looking at your problem in general (how do I deploy a python app on mac), I'm inclined to say that the answer is py2app. Basically this will bundle a python interpreter and all relevant python files for you, and give you a scriptable system that you can use to add in whatever other resources/dependencies you need.

While it's not a guide solely targetted at python/GTK+/OS X, this post is a good, detailed description of someone else's attempt to do most of what you describe. Obviously, the app-specific stuff is going to vary.