Conundrum regarding c and mass, just two thought-experiments

These are two points that occasionally cross the fault-line in my mind.

1. MASS: We theorize that mass increases with velocity, until at c mass is infinite. My question is whether this velocity is relative or absolute.

We currently have velocity, even at rest relative to Earth. Earth spinning, Earth orbiting, Solar-System orbiting, Galaxy in motion perhaps orbiting.

We can measure the change in mass for any object accelerated sufficiently, i.e. in orbit around the earth.

If velocity is absolute, i.e. if we changed the velocity to zero relative to some fixed grid in the universe, the mass would be zero, then there is a definable change in velocity that will result in zero velocity, then we should be able to calculate our absolute velocity by the change in mass when an object is in the section of orbit pro-grade and retrograde to Earth's motion vector relative to that fixed grid. Also amplified when the earth itself was moving pro or retro in it's orbit (for the purposes of the thought experiment, assuming the planes coincide with the absolute vector, but let's leave that calculation for others more capable than I). And if we can calculate that vector, and interpolate based on elapsed time, we can know "where" the big-bang occurred.

If velocity is relative, i.e. even if an object had zero absolute velocity, it would still have some residual mass due to the motion of other objects in the universe moving relative to that object, it cannot reach zero. Using the same mechanics as above, can we calculate what our current vector & velocity are, then subtract that and come up with the residual vector and velocity of the "universe grid"?

Also what is that minimum mass for an object at "rest"?

Also, if at the time of the big bang, if in fact velocity (and therefore mass) is relative or absolute has a big effect.

2. TIME

Same questions really, can we determine our absolute vector and velocity using the dilation of time with velocity.

BUT, with an odd difference.

Time dilates in the opposite direction, i.e. moves more slowly for an object as it accelerates. This seems to indicate that time is a low-energy state. If we extrapolate to an object at "absolute rest" and time is absolute rather than relative, time for that object is infinitely fast. We have to add energy to slow it down.

Correlation: If time is in fact relative, then the progression of time is changing constantly. How would we know?

Secondary correlation, if time is in fact relative, then the velocity we have calculated for the expansion at the big bang could be wrong. Distance = velocity x time. But time was not constant, it would have been infinitely fast just prior to the bang (before anything was in motion), and slowing as objects accelerated. Would that have meant that expansion would "appear" to have exceeded c when in fact it was just time dilation?

Think of two objects in a new universe. Both are completely at rest, relative to each other and relative to everything else. Neither object should have mass, and time should be infinitely fast. Now, accelerate one object. As it gains velocity, it gains mass and time slows. What happens to the mass and time envelope of the other object?

Please forgive me if these questions have been asked before. I did search the subreddit on some keywords, but did not find any relevant posts.

Thanks, hope this springs some interesting conversations.