How do I find POS of \$F(X,Y,Z) = XY \oplus YZ \oplus 1\$
Well the thing to remember is that anything \$\oplus 1\$ is simply inverted.

 A B | O
-----+---
 0 0 | 0  \_ B XOR 0
 0 1 | 1  /
-----+---
 1 0 | 1  \_ B XOR 1
 1 1 | 0  /


So you immediately simplify the equation down to:

$$F(X,Y,Z) = XY \oplus (YZ \oplus 1) = XY \oplus \overline{YZ}$$

Which is what you got. But, you could equally simplify it another way:

$$F(X,Y,Z) = (XY \oplus YZ) \oplus 1 = \overline{XY \oplus YZ}$$

Which is an XNOR gate.

In fact you can turn an XOR gate into an XNOR gate by using an odd number of inverters:

$$\overline{XY \oplus YZ} \equiv \overline{XY} \oplus YZ \equiv XY \oplus \overline{YZ} \equiv \overline{\overline{XY} \oplus \overline{YZ}}$$