I recently created a new character and then I noticed that when I deleted my old character, my new character lost its Relic Recipes and other recipes like Skeleton Key and many others in the Craft Shop. Is there a way to fix this?
I mean when I deleted the character, all the recipes that it once had, including all the recipes that my new character has are gone. Now I need to find all the recipes again which is very difficult. 
Your formulas (the ones you learned) are in formulas.gst. The file does not get deleted when you delete a char.
Is one char SC and the other HC ? Then they simply do not share them.
Im sorry but what is SC and what is HC? Can I get the formula.gst of my old character and give it to my new? is that possible?
SC = softcore
HC = hardcore
Formulas are shared between characters of the same type, meaning softcore characters share their own formulas among themselves and hardcore characters share their own formulas among themselves. But hardcore and softcore do not share their formulas between them.