Qual è la differenza tra Perdon/Perdoname e Disculpe/Disculpa/Disculpame e Permiso/Con permiso e Lo Siento, and which words are more for "Excuse me" or "I'm sorry"? ?Sentiti libero di rispondere con un esempio.

"Perdón" is usually said when asking for forgiveness, in familiar contexts and strangers as well. "Perdóname" is more personal, one-to-one situations, so you may use it with strangers but it engages a bit more in the conversation and may be odd in some situations that are casual.
"Disculpe/Con permiso/Permiso" are used as "Excuse me" even when entering buildings or any premises (especially the two latter) and are safe for both formal and informal situations. "Disculpa" is the same but more informal, personal or with people your same age or younger. "Discúlpame" is just like "Disculpa", but it is most usually used to start a conversation or asking for something, just like "Perdóname" it implies a more engaged conversation.