I want to know if I put "Mi Amore" on a sign for the name of a store would it be understood as My Love by most languages although it may be incorrect? I understand that there is a proper way to say it but would it be grossly bad grammar for a Spanish, Italian, etc. diner? What other ways can I write it?
The correct translation depends, unsurprisingly, from context. The following is a rough set of indications, with the caveat that there no absolute rules, just guidelines
If you want to use it as an epithet (e.g. "I miss you, my love, and I cannot bear to be apart from you") the correct translation is Amore mio
If you want to use it as a noun (e.g. "My love for you has never dimmed"), then I would use Il mio amore (note the presence of the article in front and the different order of the words)
Mi Amore is not correct Italian. It sounds like some weird mix of Italian and Spanish to me.