I suggest stop giving time a privileged meaning, and think of it as just one of four dimensions. John Wheeler starts his book on Special Relativity[1] by talking about surveying.

You and I survey a building (plot of land, whatever) separately because we want to check each other's work. At then end we look at our data and disagree on every single coordinate except the origin. Ah, you're a crappy surveyor, I conclude. No, you are, you reply.

Then for whatever reason I ask what distance you compute for the distance from the origin to the corner of the desk. 3.183 meters. Huh, exactly same number I compute. Okay, what about the distance from the far corner of the room to the southmost window? 18.45 meters. Me too!

A bit more chatting and it turns out you used true North as the y-positive direction, and I used magnetic North. Opps. Our frames are just rotated in respect to each other.

Now, is it freaky and weird that I say the speaker is 2.78 meters in the y direction, and you say it is 2.619? No, we are just using different frames of reference. There is no 'reality' to any given y direction or coordinate. It is arbitrarily chosen, as our the units (I could use yards instead of meters, and have an entirely different number yet).

OTOH, what is real, and invariant, are distances. That's a physically real thing. hence we always comput the same distance between any two points, despite using different coordinates for our (x,y) tuple. If you want to be mathy about it we say the metric is s^2 = x^2 + y^2. Pythagoras, in other words, in a Euclidean space.

Well, we don't live in space, we live in spacetime, where time is a dimension. When we move at different speeds relative to each other our 4-D coordinate systems are rotated relative to each other. That includes time. So, if you rotate yours relative to mine, travel for awhile (time and space!), well, you will end up with different coordinates for x, y, z, and t. It's no odder than if you and I travel 'North' in your car, but you use true North and I use magnetic we end up in different places on the globe.

In 4D space what is 'real' is not coordinates or time, but events, and what is constant is the interval between events. Just like what is 'real' in 2D Euclid space is not some arbitrary y-direction, but the distance between two objects. Distance is invariant in 2D space, event intervals (space and time) are invariant in 4D Minkowski space (the space we live in absent of gravity).

There's a bit of handwaving in there, but that's pretty much the physics; any 7th grader can do it. The main part that will lead to bad conclusions is that the metric in Minkowski space uses a negative number for time; so s^2 = x^2 - c^2 t^2. That's hyperbolic, so if you use intuition from Euclidean space you may conclude that in some instance distance will contract when it expands, or vice versa.

So, finally, to your Q1, if I travel magnetic North, is the position I reach on the "same" Earth as the one where you use true North? Feels like a weird question that misses the point, right? Same Earth, just a different location than you expected because my frame was rotated wrt yours.

Note that every experiment we have ever carried out bares this out. Accelerate a clock, bring it to Earth, that clock is younger (I'm ignoring general relativity's effects here, but the experiments don't). Measure how long a very short living particles live that are created by other particles crashing into our atmosphere, and they live exactly as much longer as SR would predict. Etc. did that clock "select" a different version of you? No, it just travelled a different path in 4D spacetime than you, and hence ended up at different coordinates. To go deeper into that I'd have to introduce "proper time", but since the ending x,y,z are the same are your x,y,z, can you see that intuitively it must be the t coordinate that changed?

[1] https://www.eftaylor.com/spacetimephysics/ This book is released under CC, free to download and share, and utterly fantastic. All you need is junior high math to master the material.