Do I have to have a separate insurance on a trailer for bikes to cover the damage to the trailer or bike?
I have car insurance need Trailer insurance to cover any damages or bike trailer I'm carrying
For the party of responsibility, the trailer becomes part the car when it is connected, so that is covered by BI and EP. Physical damage (comp / collision) must be added to your policy. Coverage needs of the bicycle itself its own policy for both liability and physical damage.
How to Maintain a Trailer : Insurance For Trailers