I mostly designed pierce oscillators. The disadvantage is that they require 2 package pins but they are fairly easy to design. The colpitts oscillator could be designed for a one package pin but - I believe - it has worse jitter performance (if this is an issue for you).
The Rbias is used to set the input impedance (it is usually a big resistor, like 500kohm). The amplifier based design will, most likely do that with some kind of feedback.
Well, R1 is often a 0ohm resistor but if the oscillator does not work (because the parasitics on the board are different from what you expected), you might want to be able to tweak here and there and this is a very simple adjustment.
you should try to kick start the oscillator (i.e. use a current pulse, say, 10nA for 10ns between ground and the gate) or try to ramp up the power supply.
yes, they are even though they have a very different behavior.
Try to have a look at this paper (a must read for xtal oscillator design):
"High-performance crystal oscillator circuits: theory and application" E.A. Vittoz, M.G.R.Degrauwe, S. Bitz
IEEE Journal of Solid-State Circuits, Volume 23, Issue 3, June 1988 Page(s):774 - 783