Madam Satya,
There is some anomaly in book example quoted by you. SBC of soil as 80 KN per sqm indicates very weak soil. Modulus of subgrade reaction that the author has worked out emperically stands for almost rock or you can say very hard soil.You can observe from the comparative table of the book that max settlement worked out from sub grade reaction is 3 times lower than that worked out for sbc.
Raft is a highly indeterminate structure. The manual one is a compromise solution and not a unique solution. The software, provided the raft is properly modelled, to a great extent, simulates the actual behaviour. SQx value can be used and is used in industry for shear checking but note to find out SQx at distance 2d from the face of the column and not the usual max one.
As reggrds mesh size, the smaller on gives the better result. Your mesh size of 0.5mx0.5m is ok.
The other gentleman Mr Arnel says that he could get the staad result close to the book solution. I doubt. For the modulus of subgrade reaction considered in the book, the staad solution can not match with the book solution. I would request him to post the file.