Is a triangle with two congruent sides always have 45 45 and 90 degrees?

No. Two angles will have to be the same and the third angle will just be 180° minus twice the smaller angles.

So if we let the equal angles equal a, and the large angle equal be we have:

2a+b=180

So there are infinitely many values that a and b can have.

a = (180-b) / 2, so the smaller equal angles have the range (0,90)

b=180-2a, so the larger has a range of (0,180)

No.

Taat triangle is right-angled (one angle = 90 degrees)

There are many triangles with congruent sides where 2 angles are equal and the other is 180 - sum of these 2, for example

30 30 120

50 50 80

40 40 100 etc ...