Hi Don,
For your 1st question, are you looking for ways to vary the bottom friction in your domain or you just want to simulate the mangrove trees by increasing the bottom friction?
If you just want to simulate the trees, probably you can have a look at this
post/discussion (and a few others) on how to implement the drag force in your domain. Though the discussions are mainly for implementing structure in the model, I think they should be quite similar to what you are trying to do.
As for your 2nd question:
to determine bottom friction computationally, there are a few roughness formula that you can choose from in Telemac. You then need to specify the appropriate coefficient for the model. Next you will need to validate your model using field data. To surmise, your coefficient values MUST be calibrated and validated using measurement data, as that's the only way to make sure the paramaters and values chosen for your model are "correct" and robust.
Hope this help
Anas