no
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Their inner angles are not a multiple of 360 degrees.
Yes - because, when you lay regular octagons together so they're touching, the space between the octagons is a perfect square.
no it cant be unless you use pentagons and octagons like on a soccer ball * * * * * That is an unbelievably rubbish answer! Tessellation - unless otherwise specified - refers to covering a 2-d surface, not the surface of a sphere. Normal soccer balls do not have pentagons and octagons but pentagons and hexagons.
No cones can not tessellate.
Yes * * * * * No. A star will not tessellate.