Binomial Model - Bond Valuation

After we assume the bond is called or put at one of the nodes, do we continue to include coupon payments?

I believe so.

In binomial model you go backward (not forward). Next period value is not dependent on last period’s bond price but they are dependent last period’s forward interest rate.

excercising call or put is just one of the possible scenarios which can happend in one of the paths of the model. In short, calling bond would not affect coupon payments along the tree.