I agree, the last name here is Groh. Back then, there was no standardized spelling of the German language, so everyone just spelled how it sounded like to them. The mother's last name is Tantzer, the -in ending is just to signify that she's a woman.
The note below that is kinda hard to read, but it begins with "1823, 14 Junius, der Taufschein ...", so something about a baptism certificate, but I cannot read the rest... I hope someone else can help.