If an author is going to create an article, he can't see the default editor I use (and can see in same case) for Joomla.
I guess this problem caused by ACL rules.
The process I followed to create a new access level for authors was under this principle: Deny everything first and then allow step by step.

So I made a new group (child of public) and then assigned them to a new viewing access level. In Global Configurations, everything is denied for them except backend login.
In K2 they are allowed everything except Configure.

How can i fix this, so they can use the default editor?

Have you changed any Joomla! settings? Which editor are you using?

I am using JCE.

As you asked me, I had an epiphany and I changed the Global Configurations from JCE to TinyEMC and now there's something strange. Even if it works with TinyEMC, I lost access on using JCE anywhere on the website (Joomla or K2) too!

Now I am pissed off at JCE, this extension is really problematic, I had other problems with it in the past. But I wonder what happened and it doesn't work now just by switching an editor? Any clue?

If you change the editor under the Global Configuration everyone, including Super admins, will see the one you have chosen from there.
If you need another Group of users to use a different editor than others you have the following options:

1) If you need your Frontend users to see a different editor than the ones using the backend you just have select for each frontend user which editor will he/she use.

2) If you need the same editor in both the Frontend and Backend but with different tools enabled you can simply use the JCE editor in the Global Configuration and through the JCE configuration enable the Frontend group. Then for that one enable or disable the tools you need them to have access to.

Well, it is not so simple. I guess that JCE is buggy because it also caused other serious problems in another website.
I had already tried what you suggest, but there must be a strange conflict in PhP level so that's why I can't solve the issue. I m leaning towards to uninstalling the JCE and installing another editor to see if the case will be solved.
I ll report back with the results.

Ok. Let us know how it went.

Ok, I solved my issue by uninstalling JCE. Here is what I did:

Tried all possible combinations of JCE. Nothing worked.
Uninstalled JCE and installed JoomlaCK (JCK).
At first it didn't work, but after I switched it to TinyMCE for super user and JCK for one of my authors, it worked!
I switched then Super user to JCK and it worked for this account too.

I guess this happened as I had to clear my cache first so any bug or PhP rule caused by JCE goes off.