A Conceptual Understanding of APIs

I have been learning coding for about a month now. I have some good experience with Python, and additionally I have completed this web development course on Udacity.

Now, I have a good foundation for programming, but one thing that confused me a lot is how to interact with various websites and APIs. The course I did briefly touched on this in terms of XML and JSON files and how some webpages offer their pages in these formats for easier reading by other machines.

But there are still a bunch of tasks which I have no idea how to approach whatsoever, but want to eventually do. I have constructed some hypothetical examples for the purpose of this question. I will post my current rough understanding of how I would do them below each one, and would appreciate feedback (on the API interaction, not on the front-end or on any back-end algorithms/AI/parsing):

• Creating a phone application (disregarding the front-end part) which can then communicate with and perform rudimentary tasks on my computer.

I have no idea how to do this, and my guess would be that I would have to look into some external application/API meant for this process and implement this on both-ends of the system.

• Being able to write a bot which goes on to a game website and controls the object via script. (e.g going onto a pacman game website written in flash and automatically controlling the character to avoid the ghosts)

I don't even know if this is possible, or how browser flash games interact handle the user-server interaction. Would I have to post some data via HTTP manually in the same way that playing in the keyboard would do? Or is everything done client side, in which case how would I fake user input? How would I get information on the ghost's position to work the AI?

• Creating a mobile app for my school by allowing users to put their username and password into the app and then having the app automatically log in to the school and fetch certain data (e.g timetable) and return back in a readable form.

I'm guessing that I would take the input from the user on my mobile-app, and then navigate to the school's login page and POST this data in the relevant forms to log in. And then that I would (somehow, not sure), navigate to the timetable URL through my code while still managing to stay logged in, and then parse the html there?

I would appreciate some detail on how these kind of things are done, preferably with reference to these examples, so that I can get a better conceptual understanding.

Thanks!

Note: I have asked all those various questions mostly rhetorically, just so that those reading can get a better understanding of what my current programming level and understanding of APIs is at. I do not expect nor require specific answers for each and every question (so I hope this doesn't get flagged as being too vague or requiring too much detail!), I just would appreciate some responses telling me roughly how each of these APIs work approximately and how I would even start at looking at how to do these things.