Can a 60 watt rms amp power a 100 watt rms speaker?

Answer 1

Yes. Those power ratings have only very loose associations with each other. The speaker's rating refers to how much power it can accept and use without damage, but that number represents the manufacturer's (and industry'e) assumption that the frequency mix coming to the speakers is "reasonable" with regard to the frequency spectrum.

In other words, if the music isn't too distorted, a condition that can come about as a result of turning the volume up too high on an amplifier that has too limited an ability to output power (which causes distortion), all will be fine, doing this with components that are as closely matched as that.

I'd like to also point out that having the power rating of the amplifier exceed that of the speakers is even less dangerous. The idea here being that lessening the probability of distortion is the key. If the signal coming to the speakers from the amplifier is significantly distorted due to the amp's trying to push past its rating (which it can easily do), the percentage of power that will go to the high frequency drivers (the "tweeters") will be higher than it should be, thus making irrelevant, the speaker's power handling rating (at least for the tweeters). In the case where the amp's rating is higher than the speaker's, the greater danger is that you'll push the speaker past its ability to handle power, which is far less likely than casing the other problem to happen. In a nutshell, don't push the system into distortion either way.