Can I use a power supply as a constant current source?(+general understating problems)
Yep, pretty much an eclectic mix here.


If a wire has 20 Ohms and handles/needs 3 A, you need a PSU with 60 V output. Your benchtop PSU can't deliver this, so the rest of calculations is a moot point;
If you use a 1 Ohm wire and set your benchtop PSU to DC 30V and 10 A current limit, the PSU will reach the 10 A limit at 10 V, and will enter "constant current mode", delivering 10 V and 10 A;
Your PSU has maximum 32 V and 10 A. Therefore, the maximum power output of 320 W will be at 32 V and 10 A. To get into this mode, your wire resistance must be 32/10 = 3.2 Ohms;
There are equations, but the answer will strongly depend on wire geometry and its orientation relative to the field of gravity, ambient temperature, airflow velocity (if forced), etc. Google for some calculations for "hot wire cutters".