Observations are not illusions. Particles moving at relativistic speeds will literally decay slower than twin particles in a lab. If a twin of yours with the exact same heart rate as you have boarded a space craft and sat still while moving at relativistic speed with you remained put, his/her heart rate would change by your measurement from what you measured before he/she left. The traveling twin, taking her own heart rate, would not notice any change at all. There are two reference frames here, two distinct coordinate systems whose displacements through space and time individually differ, but whose displacements through space-time do not differ.

Time is relative but space-time is not. You travel through space-time at speed c. You do not travel through space at speed c nor do you travel through time at speed c. Photons do not travel through time. All of their energy is displaced through space.

Yet, what I just said applies to special relativity discussions for the most part. People are often inquiring about the cosmic speedometer and how fast things go.

But what does the whole universe move with respect to? It cannot move with respect to anything else. If it did, then that anything else would be a part of the universe. Therefore, special relativity breaks down on the universal scale and we do have a special frame of reference. That is where general relatvity must take over. Gravity is space-time and gravitational waves are made out of space-time and black holes are the saturation of space-time. If you wish to observe an example of space-time structure, you can. Just watch rain drops falling from a roof top, one following another, and notice how they separate with time as they fall. The rate of their separation is 9.8 m/sec^2. Two rocks rolled off that same roof, one after the other, will get the same result.

I would discard your examples of pendulums moving beck and forth relative to one another. Pendulums cannot move away from one another at speed c. Their pivots are not moving relative to one another at all. The pendulum's arm moves relative to its pivot and the more distant a point on the pendulum is from the pivot, the faster and further it travels through space relative to the pivot, but not time. Swinging pendulums are often subjects of discussion in relativistic circles when trying to describe different forms of reference frames.

Further, be careful when thinking about dimensions. We have three dimensions that constitute volume and we have a finite amount of charges and charge carriers along with a topological structure that allows for it.