I wonder if in the same way you can do statistical analysis of human languages to determine things like which characters are vowels, perhaps if you received enough programs written in some alien brainfuck-like language you could use statistical analysis to guess which symbol is which.

If nothing else you could always brute force it; with 8 logical operators there would only be about 40,000 possible combinations. Maybe figure an order of magnitude larger number to account for idiosyncrasies in their implementation of the language. Running "hello world" a half million times shouldn't be too hard. Of course figuring out which ones are spitting out gibberish and which ones are spitting out perfectly intelligible results for one fluent in alienese would be hard. I presume they'd send a bunch of example programs that compute pi or something similarly universal, but there are a lot of potential gibberish we could fit a pattern to. It might even make sense to just keep running every code sequence in every possible combination until we get something cool.