So, now I’ve created a group which includes the four tracks and enabled ‘Selection’. But only two of four tracks can be moved together. The other two ones do not react (maybe because they begin somewhere inbetween?). Any possibility to align them to the rest as well?
all group of regions you want to move need to have the exact same lenght for that to work, try using magnetic or grid mode to trim them one by one to a same beggining - end, even so, sometimes that might not work very well when you overlap those regions with other regions nearby.
Be patient, this set of features regarding layering and grouped region selecting is still buggy but surely will improve in the future.
another thing which may help you. You can select some audio (with the range tool) and use “consolidate range” from the menu. This glues all the single files to one single block (the original is on the layers down below). This would help you to have one region per track - which would be easier to move.