I just said that vs. I have just said that

hello, i have a question about "present perfect vs. past simple"
First of all, i do a little English, actually learning English right now. Here's my question.
1. What is the difference between" I just said that" and "I have just said that"? I think in that case, there's no difference cause we can use "have just -ed" when we wanna say something happened just now.
2. I think we can use present perfect in 4 cases. can you check out whether these are correct or not?
1) The train just leaved. (=The train just leaved)
: something happened recently or just now.
2) I have eaten lunch.
: someone says what they did past to explain what they really wanna say. e.g.) I have eaten lunch = I'm not hungry.
3) I have eaten korean food.
: someone says their experience.
4) I have lived in LA for 2 years.
: to explain recently or just now someone was doing something for some period or someone is doing until right now for somewhat period.