Your position in the final diagram is quite good for white. Black has moved his queen twice in the first six moves and is already behind in development.
I don't think there is any fixed way to exploit the advantage of weak openings. Sometimes, the situation is such that the position can be immediately exploited with a quick mate or winning a pawn or a piece. But more usually it is not easy to immediately convert the advantage into something more tangible. The right thing to do in these situations is to continue to play well; continue to develop and continue to formulate a plan. For example, in the above final position I would probably play O-O.
Of course, it also depends upon what sort of weakness the opponent's opening has - it could be lack of development (as in the above case) or loss of space (which could be argued to be a little in the above case) or a blunder leading to loss of material.
In my opinion, very weak players tend to blunder away pawns or even pieces; however, for stronger players (around 1400) it tends to be lack of development by moving a piece twice or bringing the queen out too early.
If you are playing speed chess (you say you only have 10 mins) then it is even more clear what to do - you simply develop your pieces as quickly as you can and then you will find that opportunities and good moves will come easily to you and it will be more difficult for the opponent.
currently im going to study opening, but i found out that some players make the move that i didnt even see before!!
so how do we take advantage with this type of OPENING?? i have not enough time to think on how to exploit the mistakes!!! because its only 10 mins!!
any suggestions?? or these are actually small mistakes that i could only exploit it when my long-term advantage reach?? or i have to play more games to gain experience??