It's safe to sign now.
Liability to bank ==> No you won't .... you are only liable for repayments when your solicitor draws down the cheque and it's cashed. Solicitor won't draw down mortgage cheque until bank requirements have been satisfied.
The offer letter means you just accept their terms and conditions. It will outline what they need before they release the cheque .... survey (perhaps), Life Assurance being in place (not necessarily with them - get cheapest cover but if another party other than bank provides it you'll need to get it assigned to them), House Insurance in place etc.
Only time you'll be commited to purchase will be when you sign contracts.
The bank offer letter usually only lasts 3 months .... if the time expires you'll have to sign a new offer letter.