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How much does a score generally change when you add in the fifth section that you do not grade? I took a 4 section test "cold" (and it was also freezing in my room) this morning and scored a 163. Would I expect that to go down if I took a 5 section test?

Also how much would general life experience, like going to college, affect my score? I realize it would probably naturally go up, but how much would it go up without studying? Right now I'm a senior in high school. I know it's a little early to be worrying about law school and my lsat, but I'm going to an in-state college that isn't even the second most prestigious in the state, so I'm really nervous about how good my scores will have to be for any sort of graduate school.

Adding the 5th section does make the challenge of mental endurance more difficult, but I'd wager your ceiling, with a 163 cold diagnostic as a high schooler, is somewhere around 176-180, depending on your test-day luck.

Also, UG prestige doesn't matter too much, outside of perhaps the top three schools (Yale, Harvard, Stanford). Even so, you'll have a shot if you get a high enough GPA and significantly increase your LSAT by the time you take the real test in 3-4 years (which is overwhelmingly likely).

If top three is my ultimate goal, should I try to transfer to a better school after two years so I can graduate from somewhere more prestigious?

No. Save your time and money trying to transfer. As long as your school is accredited make sure you do very well, have a few softs to throw around and do well on the LSAT.