Sure, let's simplify these expressions one by one:

**a) \(x + 3 + \sqrt{x^2 - 6x + 9} \) (for \(x \leq 3\))**

Notice that:
\[
x^2 - 6x + 9 = (x - 3)^2
\]

Therefore:
\[
\sqrt{x^2 - 6x + 9} = \sqrt{(x - 3)^2} = |x - 3|
\]

When \( x \leq 3 \), \( |x - 3| = 3 - x \).

So:
\[
x + 3 + \sqrt{x^2 - 6x + 9} = x + 3 + (3 - x) = 6
\]

**b) \(\frac{\sqrt{x^2 - 2x + 1}}{x - 1}\) (for \(x > 1\))**

Notice that:
\[
x^2 - 2x + 1 = (x - 1)^2
\]

Therefore:
\[
\sqrt{x^2 - 2x + 1} = \sqrt{(x - 1)^2} = |x - 1|
\]

When \( x > 1 \), \( |x - 1| = x - 1 \).

So:
\[
\frac{\sqrt{x^2 - 2x + 1}}{x - 1} = \frac{x - 1}{x - 1} = 1
\]

**c) \( \sqrt{x - 2} - \sqrt{x^2 - 4x + 4xy + 4y^2} \)**

Notice that:
\[
x^2 - 4x + 4xy + 4y^2 = (x - 2y)^2
\]

Therefore:
\[
\sqrt{x^2 - 4x + 4xy + 4y^2} = \sqrt{(x - 2y)^2} = |x - 2y|
\]

So:
\[
\sqrt{x - 2} - \sqrt{x^2 - 4x + 4xy + 4y^2} = \sqrt{x - 2} - |x - 2y|
\]

This expression depends on the relation between \(x\) and \(2y\).

**d) \(\frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} + \sqrt{y}} \times \left(\sqrt{x} - \sqrt{y}\right)^2\) (with \(x>0, y>0\))**

First simplify \(\left(\sqrt{x} - \sqrt{y}\right)^2\):
\[
(\sqrt{x} - \sqrt{y})^2 = x - 2\sqrt{xy} + y
\]

Calculate the entire expression:
\[
\frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} + \sqrt{y}} \times (x - 2\sqrt{xy} + y)
\]

This becomes:
\[
\frac{(\sqrt{x} - \sqrt{y})(x - 2\sqrt{xy} + y)}{\sqrt{x} + \sqrt{y}}
\]

The multiplication does not cancel any terms, so this expression remains:
\[
(\sqrt{x} - \sqrt{y}) \times \frac{x - 2\sqrt{xy} + y}{\sqrt{x} + \sqrt{y}}
\]

This is already simplified in terms of basic operations.