I've understood that there are some risks with connecting pedals, amplifiers, instruments and microphones and that I should be aware of what I'm doing, or it could damage my equipment. How can I figure out if connecting something (e.g. a bass guitar to a guitar amplifier, or a microphone to an effects pedal to a guitar amplifier) is risky or not?
Is this related to signal strength? Equipment impedance? I wish I could play around more with my setup, but I'm worried about damaging it.
With decent modern equipment, it's really hard to cause any real damage by incorrect connection. Tales like “bass into guitar amp will damage it” are pretty much this: tales.
Guitar and bass amps are anyways designed to be operated outside what would be considered the “safe range” for e.g. a HiFi amplifier. Overdrive is nothing else but overloading an amp, i.e. giving it more signal level than it can really handle. Because this is so commonly done, amp designers make sure that they will handle that gracefully, i.e. simply clip the signal. Decent amps therefore survive pretty much any signal you can possibly give them from an ordinary pedal or instrument.
The only thing that you should be careful with are speaker outputs. These offer much higher voltage and lower impedance than line-level outputs, therefore they can quite possibly fry something you connect. Furthermore, tube amps can even fry themselves when not connected to a suitable load, i.e. a speaker. But, there's probably not really anything interesting you'd want to try with a speaker output anyways – these are for speakers only, which I suppose is obvious!
tl;dr don't be afraid, just try out what you want to do. Usually the worst that can happen is a loud crack when connecting, or uncontrollable feedback, so just be prepared to quickly mute the power amp whilst experimenting.
Note that the tales do have some basis in reality: old equipment not always so robust. So if you have some kind of vintage boutique amp, better sell it and get a modern amp that won't have these problems (and probably will sound better anyways).
