1) I was wondering if the floor a dog walks on becomes najjis since the dog is najjis. And also, if the floor becomes najjis does that also mean that the socks or clothes that touch said floor are also najjis?

2) Should it be removed with water or just by removing it

1) Najasah is transferred through wet touching, however, in this case, if the dogs hair or dander falls on the carpet/floor (and then to the socks) then it is certainly najis and should be removed.

2) It’s best to remove it and wash as well.