Hi Seth,
I am not a professional, but here's what I have so far. To your second point, most of the models I've seen have layered strategies. By layered, I mean that they can be broken down into substrategies and those in turn can be broken down into subsubstrategies, etc. Here's an over-simplistic example:
You have one substrategy that selects securities(buying), and another strategy that does something with them(selling). Together they make your trading strategy. First, selecting securities is usually based on either the past performance of the stock(moving average, moving standard deviation, returns, etc.), the current state (statistic) of the stock (price,volume,etc), or exogenously determined with respect to the raw market data (news, word of mouth, divine inspiration, random number generator). The second substrategy usually involves using some of the same parameters, or transformations of the parameters used to choose the security you program some heuristic that determines what to do with the stock (sets the conditions under which you will sell it). With just a simple bifurcation of a general strategy, even a small number buying and selling substrategies yields a large universe of strategies. Each substrategy will have its own unique assumptions.
Suppose that using statistics is part of both of your buying and selling substrategies, and therefore using statistics can be said to be a general strategy. Statistics is commonly discussed in the forums, so it seems like a good place to start. Within the example I just made the following would be a subsubstrategies but for clarity I will just call everything strategy whether it is a substrategy or not. https://www.quantopian.com/posts/using-poisson-distribution-to-predict-price-change , https://www.quantopian.com/posts/trading-strategy-using-markov-chainsand another Determining price direction using exponential and log-normal distributions. These examples use advanced statistical methods, and 'atypical' distributions. Each of these distributions and methods has their own assumptions, and/or conditions that should be met in their usage that can be found in mathematical texts and literature. Although it does not always show as a top search result, wolframalpha.com has been a good resource for me in the past.
Even using simple statistics carries assumptions with it, if you are using a simple mean, sum(n)/n, and/or standard deviation, you are making the assumption that whatever you are looking at is either normally distributed, approximately normally distributed or uniformly distributed. This has some implications using the API transforms mavg(days), stddev(days), vwap(days). Some of the assumptions and rules you are looking for may be in the API documentation whether implicitly or explicitly stated.
As far as the most general strategies or assumptions, there are series of constraints that may or may not be part of a model but are likely to be part of a trading algorithm. Just to put some obvious things out there, the transaction cost of making the trade, and requiring that your cash balance does not go below 0.
Another place I have found strategies, essentially listed, is in a dictionary. Don't laugh! Often if a strategy is "standard" or "common" it will be given a specific name and listed in a specialized glossary/dictionary from that field (which you may already own). This could be a simple way to get started with a list of strategies. Maybe something like Finance Dictionary or this Business Dictionary.
Also, You may not have come across this thread yet, but it has a list of articles put together by the community.
https://www.quantopian.com/posts/trading-strategy-ideas-thread
