Can we do extra prayers/rakaa/units for extra credit?
The only Contact prayers decreed by God in Quran are the five daily ones, and the Friday Congregational Prayer that substitutes the Noon Prayer on Fridays. Such prayers are decreed to be observed at specific times throughout the day:
[4:103] Once you complete your Contact Prayer (Salat), you shall remember GOD while standing, sitting, or lying down. Once the war is over, you shall observe the Contact Prayers (Salat); the Contact Prayers (Salat) are decreed for the believers at specific times.
In the above verse, we see that God commands us to remember (Dikr) God always after completing our Contact Prayers. Thus, God makes a clear distinction between Salat and other forms of commemoration or imploring of God which one could do at any time, anywhere and in any format or language.. At the end of this verse we read that the Contact Prayers are decreed for the believers at specific times (kitaban mawkota) .
The word for Al-Salah is a very specific word that is exclusively used in Quran by God to to establish contact with Him in a very well-defined format at specific times. Although Salat also is a specific form of commemoration of God, it is not the only form. With the revelation of the mathematical code of the Quran, the number of daily Contact Prayers (Salat) has been confirmed to be five.
[2:200] Once you complete your rites, you shall continue to commemorate God as you commemorate your parents, or even better.....
The word for commemorate is Dikr in the above verse as well. This (again) shows that Dikr cannot be Salat, since the word used for "commemorate" is the same word for both God and the parents. Furthermore, it is again talking about after we finish the religious rites as in 4:103.