Can est-ce que be used for requests, particularly polite or friendly ones? For instance, does this sound natural?:
Est-ce que tu peux me passer le sel, s'il te plaît ?
Yes, this is fine.
Note that there could be (at least) three ways of asking this question:
I presume your question is more about the difference between (1) and (2) than between (1) and (3).
All these three variants are fine, but the second can sound a bit more formal. Used with tu, (2) is perfectly acceptable, but may sound slightly over the top (or almost jokingly used to emphasise the request requires more important attention). With a person with whom you can use tu, (1) and (3) are virtually equivalent.
If you're particularly worried about politeness, you should be more concerned about the tu/vous distinction than using "Est-ce que", depending on the person you're talking to.
In a relatively casual dialogue such as asking for salt, these three forms would work well with vous too, although it would certainly be more important to start these sentences with "excusez-moi" (since you're likely to interrupt people you barely know or who aren't part of your current conversation, or more selfishly to grab their attention). I would say "Excusez-moi, vous pouvez me passer le sel, s'il vous plaît ?" is fine, even with strangers, considering that you'd have both "excusez-moi" and "s'il vous plaît"; using "pouvez-vous [...]" wouldn't make a big difference at this stage (even if it is a bit more formal in principle).