1. Who did the burning? mostly It is CORPORATIONs that owned massive chunks of lands (which some of the case these lands overlap with National Park territories). The rest is small land owners (which also cover big areas if you sum it). These companies though have a strong lobby in the government across layers, whether it is in the national level or province level. FYI, many of the companies are foreign ones including Singapore companies and Malaysian companies.
2. Why did the government not make it illegal to burn land? There are several factors. Actually the amount of land that CAN BE burnt is limited. However the government do not strictly enforce it, because you know, it's Indonesian government. So a step back, how come the government allow people to burn land in the first place? There is an old local bill (in Borneo area) that protect land owner to burn land. This date back to an old tradition that in Borneo, in order to farm you gotta burn the land first because of the nature of the peat land itself. I agree that in 2015, there should be a solution in making a farmland productive without even to burn it. This bill is not yet overruled and even so, being abused by corps to justified the act.
3. Another reason why there is almost no response from the Indonesian government is that the burning happened only in Sumatra and Borneo to the (North)West side (Singapore, Malaysia, Thailand). For better or worse, Java island doesn't get the haze at all, thus many politicians can't relate how bad it is actually.
What is sad is that it is the epitome of capitalism, that we can't do much about it. Palm oil is used everywhere and as long as there is a demand, supply will be there too.