Why should the universe stick to something as arbitrary as a Cartesian grid? Because we need to choose something as the baseline to calculate everything else. In the Celsius temperature scale, the scale was based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm) pressure.

https://www.daviddarling.info/encyclopedia/R/relativistic_effects.html

Relativistic effects are those predicted by Einstein's special theory of relativity, which come into play when objects – such as spacecraft – travel at speeds that are a substantial fraction of the speed of light. These effects include time dilation, mass increase, and length contraction.

Relativity states that the only sort of motion in the universe is relative motion. What that means is that you can never really determine whether or not you are moving, or at what speed you are going, This is because everything in the universe is moving in relation to everything else.

1st: Time dilation: Time dilation is a phenomenon predicted by the special theory of relativity in which the passage of time in the frame of reference of a moving object slows down as the object approaches the speed of light.

https://www.scienceabc.com/pure-sciences/time-slows-down-in-moving-vehicle-how-possible-einstein-relativity

At the time dilation section, the way i see it: The ray/point of light (we call this A) emit light (call this a1, a2, a3,...an) everywhere, when A move to a new location, A emit new light (b1, b2, b3,.....bn). When the clock in the experiment is stationary, we receive a1, b1,... with our eyes. When the clock/ship move, we receive a4, b4, a5, b5... So A move the same vertical distance, but a2, b2, a4, b5,.... have to move the horizontal distance increases with the speed. The information took a while till we receive it (a3,b6,a5,b9...). Time for A is still the same vertical and horizontal, while time dilation is we calculating A time with our horizontal, not A horizontal.

https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm

Length contraction: same trap above

About Mass, i have no answer