-- is it possible to transmit data by tx and rx?
Yes, however the tx, and rx on the Axoloti is not connected to its internal midi system, there is an object that can do this to some degree, but I myself connect Arduino tx at 3.3v directly to Axoloti midi din in. The 3.3v tx is more then adequate to receive midi through the din. Yes Arduino can also receive but if your arduino is 3.3v you will want to convert the midi out 5v to 3.3v.
-- is the arduino midi library compatible to collect this data?
I use the fortyseveneffects midi library and this works fine, I have not yet tested its USB midi library, although I do not have the need to.
-- axoloti accepts MIDI messages: NRPN, 14bits, relative?
There are quite a few different objects and discussions about using different types like those in your question, I don't use them myself, various objects use NRPN, I remember reading a discussion recently about some code written in an object to be 14 bits compatible. You may want to investigate further as there are many resources already available through posts and member contributions.
-- can the same encoder set to "gpio" move different parameters, as needed or is it condemned to a single parameter? some example?
Not exactly sure about what you are asking here, what sort of encoder are you referring too, switch, pot, rotary etc. it is very easy to store settings, use multiplexing to redirect values to other objects, math to manipulate the values for other requirements..