When you have your phone on vibration mode, you will definitely lose more power than when it is in sound mode. The vibration alert is known to use more charge during its effect hence you might be required to charge your phone often.
Yes, it does waste more battery. It takes more energy to make the phone vibrate than it does to make the tiny speakers vibrate in order to make sound. I still leave my phone on vibrate, though, because ringtones are obnoxious.
No. In fact vibrate consume about third of ring tone. I am a engineer in a company that produce both vibrator and tiny speaker. The power consumption of a vibrator is around 150mW, but it is around 500mW with speaker. In the early time of phone, vibrator was much big than now which consume more power. And there is no speaker for phone. Phone use buzzer which is much lower power to do ring tone. Vibrate consume more power than ring tone that time. But it is different now.