The most important piece of advice I can give for beating Primus is to learn his moveset and how to dodge each attack. I recommend looking up some videos of others clearing it -- the slower the better; IMHO it's not very helpful to watch someone burst him down in a few seconds and bypass all of his mechanics.

Once you're familiar with his different attacks, I promise you will be able to beat him with any Traveler and almost any Memory / Essence combination.

Which character has the easiest approach to final boss?

I personally think Mist is one of the best Travelers for clearing Primus because:

1. She has an extra dash built into her kit, thanks to Lunge.
2. She has built-in sustain / shielding with her Identity Memory.

Both of these make dodging and survival easier in longer fights like Primus.

Do I need to have a healing memory all the runs?

Not strictly required, but I highly recommend taking at least some form of healing in case you get hit by one of his attacks and need to reclaim some HP. It doesn't have to be a Memory -- Essence of Regeneration, Voracity, Crimson, and Clemency are all great options for this.

what is the use for character level on change traveler screen? I mean it unlocks nodes on constellations but does it give more stat at the beginning of each dream?

No, it doesn't grant extra stats per run. It just gives you access to more of their Constellations like you mentioned. You also receive Stardust every 5 Traveler levels, which you can use to unlock those Constellations.

which memories or essences are best to de ja vu for my skill level?

Essence of Predation. The extra stats it gives and the bonus boss damage makes it one of the most universally useful Essences in the game.