Qual è la differenza tra Perdón. e Disculpe. e Lo siento. e Con permiso. ?Sentiti libero di rispondere con un esempio.

"Disculpe"
1.when you want to apologize about a situation you don't have control. Example

"Disculpe la demora, el tráfico iba lento"
(Sorry for the delay, the traffic was slow)

2. When you will make a question to someone. (as when a teacher is speaking about some topic and you want to make him a question about it) example

Imagine the teacher talking, when you interrupts him.

"Disculpe profesor, tengo una duda"
(Excuse me teacher, I have a doubt)

Perdón

This a kind of serious apologize, to someone you hurt. Like in this kind of sorry you feel really bad about it. Ex

"Perdón, no era mi intención pisarle el pie"
(excuse me, it wasn't my intention to step in your feet)

Lo siento

I personally do not use this apology except when I want to express for a duel or condolence.

"Lo siento mucho sobre tu perro" or "Siento mucho la muerte de tu perro"

(I'm sorry about the death of your dog)

Con Permiso

Use this when you are in a crowd and you want to walk between all the people, like when you say excuse me in english.
Some people also use con permiso when you are leaving a room in a strange house where there is people. Ex.

You are introducing yourself to your girlfriend's family, all of them are in the living room, but then, your girlfriend calls you from the kitchen. So you see to the people inside the living and you say "Con permiso" and you go to the kitchen.