This topic describes how the confidence score is calculated:
The confidence values reported are for the level that is reported... so e.g., the 0.94 confidence is for the genus that is reported and you cannot infer from that what confidence you will have for family-level classification from that score.
Yes, that's what the confidence parameter in this method will do for you. In practice, you should just stick with the default (c=0.7), as it strikes the correct balance between precision/recall — c=0.95 is likely to be way too strict and result in quite poor classification. See the benchmarks here for the evidence, and how the default setting was chosen: