How to set which columns are shown in listers is covered by the Folder Formats FAQ.
I haven't had a chance to check this (I rarely use the tree) but I think the default tree width can be changed by saving the Default Lister. (Settings->Set As Default Lister.) You could also set Opus to open a Layout instead of the Default Lister, in which case you would just need to re-save that Layout after resizing the tree.
You cannot make the tree change size automatically when you enter certain folders, but you can save special layouts which go to those folders and also have different tree sizes. The layouts won't automatically be used if you go to those folders normally, though. You have to explicitly load the layouts by name.