The original MM in Detective Comics has similar power to those in House of Mistery; but also have some others very different powers.

Superman and Batman from earth 2 were ignored for much long time

I don't think Martian Manhunter's John Jones stories have ever been considered "Earth 2."  Earth 2 was mainly a device to explain how Superman and Batman had not aged by the Sixties, and also to clear up some inconsistencies in stories over the then 20+ years of stories.  You do point out some excellent differences between the Detective and House of Mystery runs, however, there is no real evidence that the writer (who by all accounts was the same throughout) intended there to be a clean break of two versions of the characters.  The powers had't really been changed, it came down more to which powers served the stories the best, which led to certain ones falling by the wayside. 
 
I was actually just thinking along these lines, what would Earth 2 Martian Manhunter be like.  I'd be very interested in actual evidence from the silver age of such a character, but I doubt any exists.  I like to think that Earth 2 J'onn J'onzz would be still on Mars, and in that alternate reality Mars would be a force to be reckoned with...

There is no earth 2 martian manhunter

MM was introduced in the mid 50s wich was the begining of the silver age thats why he was chosen to help power that tower thing in infinite crisis

The MM is a fictionary character.  As such, the only true abot him ia what the publisher said it is.  DC has never said that there are any MM from Earth2.  Until they said different, there is not a MM inEarth 2.
Any how, DC for a long long time, did not recognized the existence of a Batman, Green Arrow and Aquaman from Earth 2.  Eventually they did, and it became official.  But meanwile, the readers could foud enough differences to suspect suach existences.
In the case of the MM, there are enogh evidence to suspect the existence of a MM on Earth2; and to make posible for DC to come up with that plot at any time.
 

The MM in House of Mistery it was anounced as "introducing the new Martian Manhunter"

they were simply referring to the changes made to J'onn, not a different Martian Manhunter.

They guy made 7 post over 3 years ago. I doubt he got your message

Martian Manhunter along with Barry Allen's Flash ushered in the Silver Age so there probably wouldn't be a Earth 2 version of J'onn. I do remember reading in this book about Batman's transition into the Silver Age there was some changes to J'onn in the late 50's which could've meant bringing the Martian Manhunter to Earth 1. I'll have to find the book to explain it better.

https://comicvine.gamespot.com/roh-kar/4005-80338/