As for salat al-tawba, it is two normal rak`ahs that are prayed after one sins, which is the foundation of salat al-tawba, one asks Allah for forgiveness after it and the person may ask for whatever [s.else] he wishes for.
And salat al-awwabin, what might be intended is salat al-duha, or salat al-ghafla, as in the Tuhfa. As for duha, it is sunna and its time enters when the sun is a spear’s length above the horizon and ends at the climax of the sun in the middle of the sky, (i.e. at the beginning of the dhuhr prayer). The least of it is two rak’ahs and the most one can do is 12 rak`ahs. It is permissible to pray them in sets of two and it is also permissible to pray them all joined together finishing off with salams.
As for salat al-ghafla, it is also sunna, and its time is between maghrib and `isha. The least of it is two rak`ahs and the maximum is 20 rak`ahs. It is permissible to pray them all joined together or separated into [s. two rak`ah] sets just like the duha.