As Salamu Alaykum Ustadh is it allowed to make a trap for small animals (e.g. Rabbit) to catch and eat them while living in the forest for some days. The trap is made at night time and when time goes on, there will inshaAllah be one trapped. Does one have to say "Bismillah" before putting the trap?

Ustadh AbdulAziz al-Haqqan

No not allowed, you must do tathkiyah so if it is caught alive and you do tathkiyah then it is allowed otherwise it is forbidden.