1. the deal was the withdrawal agreement - meant to cover before the final deal.
2. it was not offered by any one side, but was the result of negotiations - here's hte picture where David Davis, a leading light on the leave side sat down for negotiations with the other 27 countries
3. The EU hasn't refused to negotiate further - it said "The UK was negotiating until November and then the agreed withdrawal deal was passed through 27 parliaments (because the eu side checked the boundaries before sitting down for negotiations) but rejected by the UK parliament (because the Uk negotiators didn't check with their parliament first, like the eu side did)
a hard brexit is unavoidable unless a deal goes through parliament - but the UK parliament doesn't have a majority for any kind of deal, so yes a hard brexit is inevitable due to the UK's confusion