Both seem awkward in English, you could say instead. I have studied English from since I was a child - You don't need to say 'to the present', as it's already implied. As for the second sentence I'm not quite sure what you want to say, could you clarify? As for the examples in the book, they're both completely correct :)

Hi -- "Since" indicates the beginning point of a time measurement (or also, it introduces an explanation: "Since you asked it, I reply" -- which someway follows the same logic of the first meaning). Your book is right: two months have passed, starting from that moment. But in that sentence you have used "since I was ill" and as it is a Perfect Tense : the action of "being ill" is now concluded, or better, it concluded "two months ago" -- so "it is two months you are healthy". If you say "I have studied English since I was a child" there is a mistake: -- "I was child" indicates a concluded period (you could also say "since childhood"): a firm "starting point" in your chronology. -- "I have studied English" is also a concluded action, but you wanted to say that you kept on studying English starting from that moment. So these are correct phrases but with different meanings: --- I HAVE BEEN STUDYING English --SINCE-- I WAS a child ---(you still do it now) --- I HAVE STUDIED English --WHEN-- I WAS a child. --- (You made it just in that moment) However, the Study is rarely "a concluded action" so this syntax sounds a bit nonsense, unless you "conclude" it, as in "I have studied THIS BOOK OF English // IN THAT SCHOOL // when I was a child" Also, you might want to consider the syntax to express that -- in a certain period of the Past -- you have kept on doing the same thing, which now you do no more: -- When I was a child, I USED TO STUDY English --- ( not now, it's a concluded HABIT) bye