After all this.. the simple answer is ..that the Namaz / Prayer is ‘Adaa’ i.e. the Farz of performing it i.e the compulsion is raised once performed.
once finished from performing it .. its upto the person ..hw much of muttaqee that person is .. his level of imaan is questioned .. if he wishes ..that he/she was distracted during namaz they may perform it again i.e. its called ‘e’aada’ with the intention that hes performing it for if there was any doubts in namaz ..this one will inshaAllah cover it.
If the person does not repeat it ..the compulsion of performing the prayer is raised.. i.e. in his naama e a’amaal .. it will be written as ‘performed’ .. but the level of sawaab will differ ..
Simple. 
As for Closing Eyes. It is Simply makrooh i.e. disliked .. meaning if its regularly done from the moment you say Allah hu akbar and keep eyes closed all the way till salam .. its makrooh ..and continuously done thru every namaz .. and made a routine of it .. its Strictly prohibited.
however, if someone does close eyes to regain concentration for a coupla seconds or so .. its jaiz .. or for example .. you are standing in taraaweeh ..and your neck becomes stiff ..then you may close eyes and you are allowed to move neck side to side or twist ..but keeping in mind that your still in prayer… or another would be which can occur with person like me that when doing imaamat ..you are reciting and you forget then you may close eyes to remember where you were reciting or what you were reciting or what comes next ..
so basically these are three main reassons when one is Allowed to close eyes otherwise seriously prohibited.
btw, thank you everyone for their input in this ma’ala, some things .. alot of ppl need to know .. and want to know ..but due to shyness or lack of conection with knoledgeable ppl ..people dont get that opertunity to learn something new about Islam. hopefully from this thread ..people learnt something and they can now practice it with confidence.