MacBook Air El Captain reset factory setting failed

After a few years, I wanted to give the mac to my daughter.

To clear all, I asked MAC per email to cancel my

ID account. They sent me an email, to confirm this.

Then I cancelled the username, going to USERS AND GROUPS,

LOGING OPTIONS etc….until I could cancel my username

I wanted to make a BACKUP, but IT DID NOT WORK

SO I GO ON WITH Reseting

Then I followed the advice to make the “factory settings”:

cmd+alt+R but then it began re-installing EL CAPTAIN again…

so I made cmd+R……now there is total chaos, because

instead of formatting the hard disk , ant THEN installing OS X

I reinstalled without formatting before…..

now it runs in a “strange mode” , usking username and password, which finally worked with "GUEST "…..

But now there are N O ADMINISTRATION RIGHTS, because there is NO USER and NO ADMINISTRATOR…..to make any changes…

I am clear to have made big troubles: THE MACE SHOULD START WITH factory setting, that means NEW APPLE ID, USER NAME, ADMINISTRATOR etc etc and now

I see a system, that is: 1) in english (my language is german) 2) I can't make any changes......!???!becouse no administrator or user fixed Please help anyone out! Thank you