The early ArmaLite AR-15 hammer,was it like the one used on the AR-10,same type of geometry and spring,or was it the same as the one used on the M16 or is it more like a before and after Colt as the later one is easy to make?

Going from this picture, I think it's based on the early AR-10 design.



This photo is from the first round of testing by the army, the one which recommended the very first changes to the rifle such as, reducing the trigger pull, adding a flash hider, giving it removable hand guards, etc.

I'd wager the entire trigger group is almost identical to the early AR-10s. The first AR-15s borrow heavily from the design of early "Sudanese" AR-10's so, it's not out of the question. The modern design may also have been invented to correct the problems the army found with the trigger during the first round of testing; heavy pull, failure to return and some such.

Did the Ar-10 had the same problems with its hammer as it did with it in the AR15?

I'm not sure. I don't know much about AR-10's.

In the AR10,the disconnector catches the under section of the hammer as in the AR-15 the trigger catches the undersection of the hammer and as the trigger moves to "rest" position the disconnector hook catches the hammer,was this change to solve the original problems with the early AR15 trigger mechenism problems?
The AR10 was used in combat and the G3 and FN FAL use a similar trigger mechenism so was the problem with the AR10 based trigger on the early AR15 caused by the the forces generated by the 5.56 as to the ones from the 7.62? or...if caused by the 5.56 ammo did the 7.62 AR10 had the same problems caused by burn filt in the bolt gas chamber as the M16?

...i guess what i am asking is,is (was) the AR10 mechanically and operationally better then the AR15 (M16)?

AR-10

Making the trigger sear double as the disconnector (like in the FAL, for instance, or 10/22) is just another way of doing it. Separating the trigger function from the disconnector function makes the parts simpler and more robust, at the expense of a bit of extra weight.

I think the AR-15 current trigger design is a simplifying modernization, and considerable improvement over the FAL and early AR-10.  Current iterations of the AR-10 are made with the simplified and robust AR-15 disconnector design.

M1 Garand trigger mechenism,one compression spring to operate all,hammer;trigger;sear.