[SR] The traveler of Tau Ceti

The Traveler of Tau Ceti
The Tau Ceti Traveler is a relativistic problem imagined by theorist Richard Hachel to describe what would happen to a traveler leaving to join Tau Ceti in accelerated mode.
We assume that the Sun-Tau Ceti system is stationary.
We set x=12 light years.
Thanks to new technology, we use a comfortable acceleration of a=10m/s² (a=1.052ly/y²).
At the start, we start all the watches. The terrestrial time is noted To=0, the rocket's own time is noted τ=0.
The problem consists first of determining what the travel time will be for the traveler, and what will be the observable times To (in the terrestrial reference frame) and apparent Tapp (what we see in a powerful telescope) noted by the sedentary observer.
The problem then consists of determining the instantaneous observable velocity (Voi) at the moment when the rocket will cross Tau Ceti, and its instantaneous acceleration measured in the terrestrial reference frame.
Finally, to determine, while we know that the rocket will be 12 light years from the earth at this instant, how far the earth will be from the rocket in the rocket's frame of reference.
R.H.