Out of four rakah sunnah before zuhar fard, if first two is finished but not 2nd two in order to cathc fard, can the 2nd two rakah be prayed after fard? or is it must to complete all four rakah either before or after fard?
From what I know, it is must to offer in whole either before or after. You cannot break them into 2 and 2 just because you had to catch up fard prayer.
From what I know, when you complete the first 2 and then you break it to catch up fard prayer, the two rakkats are automatically converted to nawafil. After Fard you pray the last 2 rakkats and then first 4 rakkats which was suppose to offered before Fard. So you will pray 4 and 4 and 2 rakkats as they are suppose to be. You can't break them for any reason.
Someone may correct me if i am wrong.
I do follow the fiqh of Hanafi. So, I will answer you from the perspective of Hanafi Fiqh.
If you have small amount of time remaining for offering 4 raka'ah salat before 4 raka'ah fard of Zuhr or missed the few raka'ah of fard salat of fard and attending it as masbooq, then, you can offer the 4 raka'ah salat that you missed previously after offering 2 raka'ah salat of sunnah which is generally offered after 4 raka'ah fard of Zuhr.
In a nutshell, in Zuhr prayer time,
4 raka'ah sunnah -> 4 raka'h fard -> 2 raka'ah sunnah (Most general form)
4 raka'ah fard -> 2 raka'ah sunnah -> 4 raka'ah sunnah (which you missed previously)
Allaah knows best