To me, there are only 3 dimensions, that of space.
That does not mean the relativity math is useless. On the contrary, what they describe is real and we can experimentally verify it.
But that does not mean we can 'move' into time, as we 'move' into space. That's why time is not a dimension.
Spacetime simplifies many things for example in that framing nothing is ever at rest or nothing ever travels at different speed. The speed of everything is the same, it's just that things spatially at rest have all their speed in the direction of time. Accelerating something in spatial direction is rotating (mathematically) their motion away from time direction, into some spatial direction. This requires energy so the time direction is lowest energy but to rotate it away from it you need to put in energy. If you want to rotate it to 45 deg you need infinite energy.
Exactly. Time is just a very useful fudge to describe change. If nothing changes, there's been no time. If something changes, there has been time.
A dimension is just a useful number that you can operate on. You can have a physics where the fourth dimension is how blue something is, and the fifth dimension is how good Mary thinks it tastes.