When I was doing maths at university, I very often found that I couldn't quite prove something I had to. Being very sneaky, I would then do a bit of proof, write a little bit of incomprehensible gibberish, and then write the last couple of lines assuredly saying that the problem was solved. I get a little bit worried that proper philosophers might do a similar thing. In particular, the approach on this site very often seems to be to check that an argument about, say, morality matches our preconceived ideas. So I guess my question is how much can I believe what a philosopher says when I don't understand part of their argument? PS - my sneaky exam technique didn't work very well :(

You bring up several interesting points: (1) Sometimes philosophical arguments are hard to understand. This is to some extent par for the course: problems in philosophy are hard, and the arguments often sophisticated. Mental effort is required in order to grasp what is going on. Doing philosophy, like acquiring many forms of knowledge, is often hard. (2) Sometimes philosophers write in an unclear way. This is undoubtedly true and also a bad thing. Sometimes philosophers write in an obtuse style, sometimes philosophers do not take enough time to revise the presentation of their ideas to make them clear, sometimes philosophers only have inchoate ideas which require effort on the reader's part to develop. (3) It is possible for there to be no argument at all, only gibberish. This, although possible, goes against the entire point of doing philosophy (just as 'proving' a result in mathematics by writing down gibberish goes against the whole point of proving results in mathematics). The point of...

Is there any test in philosophy to verify or refute the philosophers' guesses/hypotheses?

There are data that philosophers aim to respect, and their guesses/hypotheses may either fail to fit, or succeed in fitting, this data. Unfortunately, there is not a great deal of consensus in the philosophical community on exactly what this data consists in. However, many philosophers would like to count (i) our best scientific data, and (ii) many of our common sense intuitions, as data that their hypotheses should respect. One major difficulty is that it is often not possible to fit all the data at once: philosophical hypotheses may explain some data at the cost of ignoring others. Another difficulty is that there can be more than one hypothesis that explains the data, and it can be difficult to tell which explains the data best.