I would like to get a PPL at some point. However, because of costs, that's likely to be years in the future, if ever. I know I'll take a course that covers what's on the written test as part of getting the license, but I would like to start studying online before then so I'll already be familiar with the topics. Are there any no-cost (and preferably open-source) websites or Android apps for studying?
Probably the best place to start is the FAA's Pilot's Handbook of Aeronautical Knowledge, (PHAK). You can find it here: PHAK You can also purchase paper copies on-line or at a local flight school if you prefer.
You will also need to be familiar with the Federal Air Regulations, (FARs) in 14 CFR, (Code of Federal Regulations). In particular, parts 61 and 91 of chapter I. I have found Cornell University's legal website most useful for searching these: FARs
And finally there is the Aeronautical Information Manual, (AIM). You can find PDF versions on the FAA's website, but I have always used the paper version, published annually, bundled with the FARs, and referred to as the "FAR/AIM". They don't change much, so while you will want the latest when you are doing final study prep for the written, for early learning and high level overview you could probably get an outdated paper copy for free or very cheap if you want to mark it up and add tabs, etc.
I would start with these as the "big three". Of course there are other resources as well, but these will get you off to a good start.
There are any number of "Online Flight Schools" that can be found by using a simple search on your favorite search site.
Some appear to offer a fixed price for the course, others offer a monthly subscription. Some appear to offer guarantees that you'll pass the written test.
No cost? Not really other than there are multiple resources available free from the FAA web site that have all the information that you need to know to pass the written exam.
FAR/AIM - FAA FAR/AIM
ACS - FAA ACS
As well as many others. There are also sample exam questions:
The problem with the FAA site is that it's very easy to drown in information. An organized course can help you focus on in the most important topics that you need to pass the exam.