Since i'm not an experienced player i can't talk about balance and improvement, still, i can see that there are a few things that might be added to make the game even more interestiing and new players friendly.
1) The skill tree it's not a skill tree. Usually the point of skill tree is to let people speialize in something but there is not such a thing here since you just have to grind you way till the end and you are done. My suggestion would be about
1a) making more specialized braches. Now with a branch you specialize everything about that sector ( like all the firearms + melees for the weapon one) and i feel a little boring not being able to master the weapon or the stat you like (like shotgun branch, sniper branch, melee branch and so on).
1b) giving limitation on the abilities you can have. Acually as the game is now it's good for balance, still, it lack the dinamicity of a game in which you can change your playstile based on the abilities you choose. This can be archieved just by using a "level" system (or simply imposing an experience CAP): every time you level up you get skill points and you use those to get the skill from the branches you prefer. Ofc end branch abilities are stronger since you need to get all/most of the brach before you can buy the skill (and maybe they are also more expensive).
1c) since you would need a lot of time to grind a new character to change your tree, a shop item for the reset need to be issued (it gives you all your points back). Also since this is an important feature after you cap your level (or maybe even before) you can exchange surplus experience for a reset skill pill (also depending on how much it would cost it might be good to add it as an extra rare item for difficult stuff)
1d) eventually adding levels to the abilities (with a CAP) and having a minimum level required to get access to the next still might also be good to increase the different number of combinations
2) Add /make a mod with more different zombies. Actually zombies get boring after a bit since the normal ones are easy to deal with even in big crowds and super zombies are (for what i saw) just dealt by shooting from a safe place (not to mention that they are a cancer for newbies because of their insane hp pool). So i was thinking that adding several zombies like spitters, sentinels (higly sensitive ones that alert other zombies), runners (vey fast melee ones), tanks ( slower but study), bombers (you just enter a builng and boom a zombie hidden behind the door gets near you and after a bit explode), fakers (zobies that seems "dead" but that when you are not whatching just get up and start attacking you (bad for the weak of heart)) and so on. This way the PVE might result much more interesting and not just something you do to farm while pvping)
2b) With new zombies it would be nice to have an Hardcore mode where raiding it's going to be super hard even in a group (with good rewards and maybe with shared inventory with the survival/open world mode)
2c) if the PVE is going to become very interesting also a super hard mode with pvp off migh be issued. There the problem won't be players but extremely coordinated zombies (not with excessive health but high in numbers and with tricky zombies combinations everywhere)
3) a tutorial. when i started i had an hell of a time to understand how you should play and to discover stuffs like skills and the global inventory. For that you can just create a small guided tutorial in the menu and a gamplay guided tour that explains you the keys and the basic objects/weapons (for that just cut a very small piece of map and add some zombies making the players kill them with different weapons).