With Family Search, you should look to see if there are any sources associated with the information. For his birth, it appears that there are 7 sources, but when I clicked on it, none supported a 1701 birth date.
As for Hannah Holbrook, clicking on the Sources tab for her show all entries related to Martha Ives. It is interesting that on October 13, 2020, her name was changed FROM Martha Ives to Hannah Holbrook. I'm not sure why, but you can send an email the the person who changed it if you'd like. You can also make a change yourself to Hannah's name on Family Search to restore it to Martha Ives. You can also correct Daniel's birth date as well.