The form should accurate. I've just taken a look at the blank form - Law Society Fixings and Fittings form Edition 3 - and there is nothing on the form that the BUYER signs - only the seller(s) signs.
Your solicitor asks you to confirm that it is right, and you have told him what errors are. Provided all the things you expected to be INCLUDED are listed, I wouldn't get upset about it - it is their stupidity.
You should ask your solicitor for definitive advice - but my non-legal view is that are not binding yourself to anything to your disadvantage, unless you are concerned they may leave garbage white goods that you have to dispose of.
A burglar alarm, if fitted, should be listed as a fixture, lest they attempt to remove it.