cjackson said:
Is it possible to build a vehicle that can accelerate to .99 C?
Theoretically yes.
cjackson said:
How would we go about doing something like this?
No time soon, it would require fantastic advances in technology that don't look to be anywhere on the drawing board.
cjackson said:
If at all possible, how many centuries or millennia is it before this can be accomplished?
Same answer as above.
cjackson said:
Could a Bussard scramjet do it?
I take it you mean "ramjet" and no,
http://en.wikipedia.org/wiki/Bussard_ramjet#Discussions_of_feasibility".
cjackson said:
How large would a laser/maser/gaser have to be to get the craft up to such speed?
http://en.wikipedia.org/wiki/Beam-powered_propulsion" .
cjackson said:
How long would it take from the crew's perspective to cross the galaxy?
At .99c time dilation is 0.07 minutes for every minute for an observer at rest. To cross from Earth to the far side of the galaxy (~70kly) would take 4962.168 years from the perspective of the crew. From one side of the galaxy to the other (~100kly) would take 7088.821 years.
cjackson said:
How big would the craft be? I imagine a lot of fuel would be required even if you could gather propellant along the way - Bussard scramjet. What kind of fuel would be needed?
That question can't be answered because it depends on technologies that haven't been invented yet e.g. how much mass do you need to hold the necessary stable ecology, industry and society. As linked above ramjets would not work.
cjackson said:
Would such a vessel help establish a galactic civilization? Or would time dilation make implausible?
In addition to such a vessel you would also need to be able to terraform otherwise you're not going to have a civilisation. Whether or not it could work as a civilisation is anyone's guess, see the http://en.wikipedia.org/wiki/Fermi_paradox" for further discussion.
cjackson said:
The ship or civilisation? Either question is as unanswerable as a Neanderthal trying to envision Facebook.
cjackson said:
Are any sort of warp drives completely impossible?
On the subject of warp drives http://arxiv.org/PS_cache/gr-qc/pdf/9905/9905084v5.pdf" . The "trick" is to change the warp bubble so that it's exterior radius is microscopic yet the interior radius is large enough to accommodate your vehicle (essentially making a warp bubble that's bigger on the inside than on the out). Apparently this would greatly shrink the amount of energy needed to manageable levels. They don't outline how exactly a shell could be build around a ship in such a fashion nor how the ship could leave.
However neither of these approaches fixes the other problems of a warp bubble such as requiring the construction of an exotic matter shell, superluminal signalling to steer/control the bubble and the huge amount of radiation a warp drive subjects you to. There are some interesting (but technical) objections in http://arxiv.org/PS_cache/gr-qc/pdf/0406/0406083v2.pdf" that apparently show that a warp drive would only be capable of very low velocities as well as highlighting other problems.
In summary unless you have a way of making speculative impossible exotic matter, it's not going to happen (and might not even if you could).
cjackson said:
If so, which of the following would best for interstellar travel: beamed propulsion, matter/antimatter reaction, Bussard scramjet, or something else?
None of them. For manned interstellar travel beamed propulsion won't be strong enough, M/Am rockets are far too dangerous (your "vessel" is a weapon so powerful that it could easily annihilate the entire surface of Earth countless times over) and the Bussard ramjet won't work.