Earth-Globe Riddles

We think of the Earth as a perfect sphere. I have three problems, fortunately we won't need sketches!

The following are our problems

1. The complete triangle mystery

2. Furthest place on Earth

3. The date line and time travel paradox

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The Questions

1. Starting at a given point on the globe you proceed 550km North, then 550km due West, from there, 550km South then finding yourself at the initial point again.

Where are you? This is not so hard.

2. Given your exact location on the Earth's surface, what is the furthest point on the globe from your current position, from your exact longitude and latitude. Or, what is the furthest, shortest distance from a given point on a sphere? Can you find yours?

My own calculations turned out as from here to be Hawaii. Where am I now?

Strictly speaking this probably warrants proof but the result is quite clear. Also to think about, that old story the shortest distance between two points is a curve! Obviously then because of constraints.

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3. A bit more tricky. My reasoning is as follows, when I cross the date line the date changes, so theoretically if I cross it in the backward direction I am in the previous date and then circling the globe I am in that same place again, and if I cross once more, another day into the past. Carrying on in this manner I can theoretically travel to the past and to any day. Depending where you are on the globe this all can happen very quickly! It might be easier to think in terms of hours not days.