I just lost everything I wrote as I submitted it, so now I'm going to type it again... 了 indicates some sort of change. That change could have been brought about by an action completed in the past (which we would use past tense to describe), but not necessarily. For example, 现在下雨了 is more likely to mean "It is NOW raining (whereas it wasn't before)" than "It rained". When you see 了, you have to realise some sort of change has taken place and then figure out if that change was the completion of an action or if a new action started happening. 了 exists in a lot of other sentence structures as well, so if you see 了 this isn't necessarily what you're dealing with. 过 indicates that the subject has the experience of completing the action. For example, you can read 我去过中国 as "I have the experience of having gone to China". This is similar to present perfect in English, but not exactly the same. The biggest difference I think is that you can state a specific time with 过, but you can't in English ex. you can't say "Three years ago I have gone..." in English, but you can say 我三年前去过中国 in Chinese. I'm only a learner myself, so I could be wrong. Take what I've said with a grain of salt.

过 means I have eaten it （a experience） 了 is used to express a condition that I have just eaten it and, it is a kind of omission of 过了

我吃過 I have eaten XXX in the past and have the experience of eating it, then main point here is what you have experienced to eat,emphasizing what you have eaten 【我吃過漢堡】 I have the experience of eating hamburger. 我吃了 I have completed the action of eating XXX, then main point here is you have completed the action 'eating‘,emphasizing what you have eaten 【我吃了早飯】.I have completed to eat my breakfast. 我吃過了 I have completed the action of eating XXX and have the experience of eating it, the main point here you emphasize you have completed the action of eating something but emphasizing the action of eating, not what you have eat 【我吃過了】 I have completed my action of eating. But 【我吃了】 itself can also be used with same meaning of 【我吃過了】sometimes.

There is no" 我吃過” in Chinese. Actually it is totally same in Chinese, and its just a bit different when we native Mandarin speaker say it. We use "我吃了” when people ask "Have you eaten ~" We use "我吃過了” when people ask " Do you like to have some~ (foods)" Ex: A:你吃了嗎？ B:我吃了。 A:你要吃麵嗎？ B:我吃過了。

You should not learn Chinese in the way you use! Just forget all these rules.Remember and practice with native speakers.Practice makes Perfect! In Chinese,there is no "我吃过“It is weird. 我吃了 and 我吃过了both ok! same meanings. You also can add something after 我吃了，我吃过了。Like 我吃过了早饭/我吃了早饭。