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Roughly how much land does the average person in Mongolia have to themselves?

About 50 hectares

Mongolia is about 1.56 million km2 with about 3.5 million people, giving about 0.45 km2 each. A km2 is 100 hectares, so roughly 45 to 50 hectares per person, the lowest population density of any sovereign country.

Which countries are landlocked by other landlocked countries, so you must cross two borders to reach the sea?

Liechtenstein and Uzbekistan

Liechtenstein is ringed by Switzerland and Austria, both landlocked. Uzbekistan's neighbours are Kazakhstan, Kyrgyzstan, Tajikistan, Afghanistan and Turkmenistan. None has ocean access, since the Caspian is a lake.

Which two countries share the longest continuous land border?

Canada and the US

The Canada-US border runs about 8,890 km including Alaska. Kazakhstan and Russia are second at roughly 7,600 km, and Argentina and Chile third at about 5,300 km.

Which country has the most wild camels?

Australia

Camels were imported for desert transport in the 1800s and released when motor vehicles arrived. Australia now has the world's largest feral camel population, in the hundreds of thousands.

Which landlocked country has among the highest GDP per person in the world?

Luxembourg

Luxembourg regularly tops GDP-per-person tables at well over 100,000 dollars, driven by finance and by cross-border workers counted in output but not population.

Which sovereign country receives the fewest tourists each year?

Tuvalu

Tuvalu receives on the order of 2,000 visitors a year. There are only a couple of flights a week and the runway doubles as a public space between them.

Which country's national sport involves teams trying to carry a headless goat carcass to a goal?

Afghanistan, with buzkashi

Buzkashi is played on horseback across Central Asia and is Afghanistan's national sport. Matches can involve hundreds of riders and last for days.

Which country's territory is closest to the sea everywhere, having no point far inland?

Singapore

Singapore is about 50 km across, so nowhere is more than a short drive from the coast. The point on Earth furthest from any ocean is in Xinjiang, about 2,500 km from the sea.