Long answer: You can do this because whenever you use findViewById() to get a reference to a part of your layout, the method only looks for that view in the currently inflated layout. So even if you have another view with the same ID in another layout, Android will not look for it there.
It is recommended that you use different ids for different layouts. On the long run, when you will have a lot of layouts and therefor a lot of ids it will get very complicated to differentiate them.
I usually name my ids like this: layoutName_elementId.
It works for me to easily find the id I'm looking for, especially when using autocomplete (I know on what layout I'm working, but I don't really know the id; in this case, with my naming strategy, I only type the layout name and it brings on all the ids of that layout).
More information on layouts and ids can be found here.
An ID need not be unique throughout the entire tree, but it should be
unique within the part of the tree you are searching (which may often
be the entire tree, so it's best to be completely unique when
possible).
So the short answer is that it's not mandatory but it's a good practice to avoid possible conflicts.
Not recommended, because if in future you will need to refactor the viewid, Android studio will refactor it in all XML files and classes and you will get into trouble.
But there are also some cases when you do need to use same id for example if you have some abstract and you reuse multiple layouts.
In case you have multiple views with same id's in your project and you need to refactor, do it manually, don't use build in IDE function, change the id in the target view inside XML layout then fix the red error inside layout.
Update:
Currently Android studio support refactoring with "refactor in current file only" option.
Update:ViewBinding
You can get casting exception if you have nested layouts (include tag) with view id's that clashed with id's in his hierarchy.