Question

isosceles triangles are always similar to each other

Answer 1

No.

Imagine that you are making an isoceles triangle out of two metersticks that you hold against the floor -- the floor is the third side.

Hold the ends of the metersticks up pretty high with their ends together at the top and about 10 cm apart at the bottom. That's one isosceles triangle.

Now hold the ends of the metersticks down pretty low with their ends together at the top and far apart at the bottom. That's a second isosceles triangle.

They are not similar.