Will Android shift Google Calendar events when I go to different time zones? I'm entering a bunch of events into my Google Calendar on the web interface and am wondering if I should do them all in local time or select the proper timezone.

If I explicitly pick a timezone (e.g. 1 PM PST) and it shows up as 4 PM EST, will it "fix" it when I go out to California?  What about events with different starting and ending time zones?
Yes, at least for me. All of my events are stored as GMT and the time of the event is displayed based on the time of the device (my location). 

Now, I don't know what happens if you "specify" the timezone like you mentioned, as I have never done that.