Voltage/Current waves on N port networks
How should I fix the directions of voltage and current to calculate powers?


The usual convention is what's shown in the diagram.

With this convention, if \$\Re\lbrace V_1 I_1^*\rbrace\$ is positive  then port 1 is absorbing power and if it's negative then port 1 is delivering power. Similarly if \$\Re\lbrace V_2 I_2^*\rbrace\$ is positive then port 2 is absorbing power and if it's negative then port 2 is delivering power.


  Is the output power at port 2 equal to Po = 1/2 Re{V2 I2*}, or Po = 1/2 Re{V1 (-I1*)}?


The power absorbed by port 2 is \$P_2=\frac{1}{2}\Re \lbrace V_2 I_2^*\rbrace\$, and the power output from port 2 is \$P_{o}=-P_2=-\frac{1}{2}\Re \lbrace V_2 I_2^*\rbrace\$.