Question

Equilateral triangles are always similar to each other

Answer 1

yeah

Answer 2

Two triangles are similar if: 1) 3 angles of 1 triangle are the same as 3 angles of the other or 2) 3 pairs of corresponding sides are in the same ratio or 3) An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio.
So if they are both equilateral, then they both have three 60 degree angles since equilateral triangles are equiangular as well. Then number 1 above tell us by AAA, they are similar.

Answer 3

true, because all equilateral triangles internal angle are 60 degrees.

and you know already is two triangles have 3 same angles, they are similar :)