Here is a perspective to understand the fourth dimension.
Like moot said, sometimes our words or our preconception of what a certain word "means" can detract from our ability to understand or describe the phenomena. (At least that was my perception of one of your points, moot. hehe)
Instead of "time" substitute the word "duration".
To "continue" or "to last". (Avoid definitions of duration involving the word "time".)
With this "arrow of time" superimposed or "layered" over the first three spatial dimensions, objects "exist" within these dimensions.
Without "duration", no physical object can be said to have ANY of the attributes or characteristics of the three spatial dimensions.
Drat...work time...gotta run.
Stupid time! Ugh!

Regards,
Sun