Always and without fail sign POA or Guardian or HCP after your name. If you sign your name without those, you could be stuck for the bill. NEVER sign a blank form. Always get copies of every document you sign, just in case you do need to see a lawyer later. (I am a Notary Public)
Well, before you sign the bill you should read the bill, so take your time, understand each section, think about how it may apply to a worsening health condition(s). A lawyer will charge a lot to do that, and what are they going to do, if there's something unusual? Most NH are rigorously reviewed by their state anyhow. The devil is not the entrance paperwork, it's how they get interpreted later on. there'll be periodic "reviews" and updated level of care...with corresponding rate increases. The paperwork when you enter might not lay it all out as explicitly as that but, if the resident needs more care then their bill gets higher. We had a relative with dementia who by the end was at the very highest level of pay. When they entered the NH we had absolutely no idea the bill would ever get that high. But it happens. It was a very very good NH and we had mostly good things to say about our relative's care.
Always get copies of every document you sign, just in case you do need to see a lawyer later. (I am a Notary Public)