We can make duas during salaah. There are specific duas that can be recited while in sajood, between prostrations and other places. if you go through this book
http://makedua.com/ it mentions which duas can be recited where in the salaah. As for making personal duas within the salah, i've been hearing different things so i'm not sure.
According to islamqa:
Making du’aa’ in English or in any other language is permissible outside of salaah (prayer). But it is not permissible to say any part of the salaah in any language other than Arabic, according to the majority of scholars.
But if the Muslim can stick to Arabic in all cases, especially in acts of worship – and du’aa’ is an act of worship – that is preferable and is better.
http://www.islamqa.com/en/ref/11588
http://www.islamqa.com/en/ref/20953
OK so no duas in any other language within the salah but if it's in arabic then it's ok, however, best duas within salaah are those from the Quran and the sunnah.
That is my understanding of this, inshallah if someone knows more about it then they can share it with us here.