To what extent are the mentioned hadiths, which speak of the forgiveness of sins even if they were like the foam of the sea, authentic?

The first hadith is authentic (sahih), and the second is authentic according to Muslim's criteria (sahih ala shart Muslim). The third is good (hasan), and the fourth is rejected (munkar). The fifth is authentic (sahih), and the sixth was narrated by Ibn Hibban. The seventh is weak (da'if), and the eighth was mentioned by Ibn al-Sunni and al-Daylami. The ninth is weak (da'if), and the tenth has not been found. The eleventh was mentioned by Ibn al-Sunni and 'Ala' al-Din, and the twelfth is weak (da'if). The thirteenth is weak (da'if), and the fourteenth was narrated by Bukhari and Muslim. The fifteenth is weak (da'if), and the sixteenth was narrated by al-Tabarani with trustworthy narrators. The seventeenth was deemed weak by Shu'aib al-Arna'ut. It is permissible to act upon weak hadiths concerning virtuous deeds (fada'il al-a'mal) if their weakness is not severe, and with other conditions.