Does the power dialer or voicemail drop cost extra?

No. There is no extra charge for the power dialer or for voicemail drop. You pay only the normal per-minute phone rate for the call, the same as a regular call placed from the browser.

Any call on the web phone, whether you talk to a person or to a voicemail machine, is talk time. When you drop a voicemail, the length of your recording counts as call time.