What is the difference between 已经 and 过 ?Feel free to just provide example sentences.

过 has many meanings and I guess you are specifically talking about the case where it has the same meaning as “已经”. They are identical. To make it easy to understand, consider the example "I have already had breakfast" "I already had breakfast" and "I have had breakfast" All sentences are the same. The "have done" can be expressed as "已经” in Chinese. The word "already" is the same as"过". You can use either of them or both of them.
我已经吃早饭了=我已经吃过早饭了=我吃过早饭了。
The first and last one are grammatically correct, the second one is tricky because grammatically speaking, 已经and过 are the same, which means one of them is redundant. However, this expression is the most common used oral expression, so it is grammatically wrong but everyone used it. The third one is also a common expression, the first one sound a little bit weird, less people use it