No.
Each interior angle of a regular pentagon is 108 degrees. In order for tessellation to be possible, the sum of the angles meeting at a point must be 360 degrees. That is to ensure that all the space around that point is covered. But 108 is not a factor of 360 so it is not possible.
Yes
No a pentagon is a single polygonal shape, A tessellation is a scheme for covering a plane, without gaps of overlaps, using multiple copies of the same basic shape. These are usually polygons.
regular hexagon
Yes
It is a regular tessellation.
A regular tessellation or semi-regular tessellation or none.
Yes
There is no such thing as a seni-regular tessellation. A semi-regular tessllation is a tessellation using two regular polygons: for example, octagons and squares together.
No a pentagon is a single polygonal shape, A tessellation is a scheme for covering a plane, without gaps of overlaps, using multiple copies of the same basic shape. These are usually polygons.
A regular tessellation is one in which a plane is covered, without gaps or overlaps, using copies of a regular polygon.
Semi-regular tessellation is a tessellation of the plane by 2 or more different convex regular polygons. A semi-regular tessellation combines two or more regular polygons. Each semi-regular tessellation has a tupelo, which designates what kind of regular polygon is used.
regular hexagon
Yes
No. Regular tessellations use only one polygon. And, according to the strict definition of regular tessellation, the polygon must be regular. Then a tessellation using rectangles, for example, cannot be called regular.
Yes. Bees are extremely good at tessellating regular hexagons in a honeycomb.
It is a regular tessellation.
No. See, for example, the top image in the attached link.