That is the correct spelling of "timesaving."
Timesaving, time saving, or time-saving; could all be used.
yes
timesaving message media
timesaving message media
It is not hyphenated.
Motorcycle is not hyphenated
No it's not hyphenated.
words are only hyphenated when they have a separate meaning when separated than they do when hyphenated
No, "hardworking" is not hyphenated.
Yes it should be hyphenated.
It can be. Some words can be seen both hyphenated and non-hyphenated.