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Keep in mind that you are not seeing a complete "half" of the earth in this picture. As your distance increases, the effective horizon encompasses more of the surface. Only at infinite distance would you see exactly half of a sphere (mathematically speaking).

Try taking a picture of your globe closer and closer to the surface and watch as less of the surface is visible in each.

Yes, they do. Try orienting the globe for yourself here:

https://www.echalk.co.uk/Science/physics/solarSystem/Interac...

You're right! But with my globe at home, and that site you listed, at the same angle I can clearly see part of India and Australia, it's weird that they don't seem to show up in this picture.

If you get closer and widen the lens, you will see an arbitrarily small portion of the earth as you approach it.

The Pacific Ocean is enormous.