If you get really close to the speed of light (which is not really practical from a materials engineering standpoint) your time of transit is significantly shorter.
Once these (extremely hard) engineering problems are solved, a trip to the next star can be a week-long affair from your point of view, but your friends back on Earth won't see you for about a decade.
Unless my math is very wrong, at 0.9c the passenger perceived time is more or less half the perceived time from the departure point. That's already quite significant, although not something I could do over a vacation ;-)
In order to spend a leisurely "cruise-ship" week to Proxima you'd need to go very close to c. At that speed, even friction with a non-ideal vacuum is a problem :-D.
Nope! If you obtain the full speed of light then a) you're not made of baryons anymore so congratulations on that and b) no time passes whatsoever between your being emitted in some tight laser beam on planet A, and being transcribed on planet B, from your perspective.
None. Photons don't experience time, they are time.
Not exactly. For you to think you are traveling 20x faster than light, your friends that stayed at home would have to see you traveling at 0.99995c. For 233x faster than light, that's a lot of 9's in that number.
If you get really close to the speed of light (which is not really practical from a materials engineering standpoint) your time of transit is significantly shorter.
Once these (extremely hard) engineering problems are solved, a trip to the next star can be a week-long affair from your point of view, but your friends back on Earth won't see you for about a decade.