"golchi" is to wash and "glanhau" is to clean. They're not really interchangeable and also "golchi" usually needs to you specify what was washed, for example: Dydd Mawrth dw i wedi golchi'r dillad. Tuesday I have washed the clothes.
I wouldn't have thought so. The impression I got was there are certain idiomatic expressions where "dydd" can be omitted, because it is implied. (Morning and afternoon are after all times of day) I would not expect that to be the case here though.