It's important to bear in mind that there's more student accommodation in Liverpool than there are students. Housing week is held in February, and though it is a bit of a mad rush as people scramble to find accommodation, don't be panicked into taking a house you feel unsure about before then - as ultimately it's you who will have to live there for a year if things go wrong!
If you do end up with a contract you have concerns about, you can contact LSH who will be happy to check it over before you sign.