OK, the first thing is that the original sentences are correct. There's nothing wrong with them.
If you want to know whether a phrase is common (or correct), you can search for each phrase in quotation marks. For example, search for "take some weeks off", then "take off some weeks".
I already know the answer, but I'd like to know how your search goes. ;)
The second sentence uses past perfect, which explains why your suggestion is impossible. If you wish to start the sentence with "to...", you need to rewrite the whole sentence instead of changing one part.