Is this a parallel circuit? How can I tell whether it's parallel or not?
Starting from one terminal of source, if current has more than one path to reach the other terminal, then those two paths are parallel. I see two such paths in your circuit. 

You didn't say how you calculated \$I_x\$ and \$I_o\$. The answers you got are wrong. Try Current dividision.  

EDIT:
You used 4A instead of 6A in your calculations. 

If you want to find the current by dividing voltage across resistance by resistance value, you have to find the voltage \$V_o\$ first.
$$V_o = 6A\times (1\Omega || 2\Omega) = 4V$$
now,

$$I_x = V_o/1\Omega = 4A$$
$$I_o = V_o/2\Omega = 2A$$