Correct. The English word 'wake' could mean 'to stop sleeping' or 'the trail left in the water by a ship'. It's not entirely strange for a word in another language to be polysemous.
Honestly can't remember what the context was. Something's changed since then.
Should "i am reading ..." be "ik ben aan het lezen"? If so, where does "een heel boek" fit?
Progressive tense in English could be expressed in a variety of ways in Dutch. Your way is more appropriate if you want to emphaisize on the continuity of the action. Please try not to make one-to-one mappings with grammatical concepts across different languages; it simply doesn't work. On the 'een heel boek' part, you would place it right after 'ben' - 'ik ben een heel boek aan het lezen'.