I tried destroying an anomaly with a warship and that wouldn't play, so that answers the question whether they can be destroyed.
Next question, do new anomalies keep appearing as the game goes on, or are they fixed in place at the time the galaxy is created, the same as stars and planets?
Next question, can more than one civilization discover and get the benefits from the same anomaly, or can they only be used once?
Thanks for your replies.