As far as I know one can't reduce the chance of disasters to 0.

Kings cannot hand out fiefs for free.

The only differences between fiefs are:
- the number of buildings already there; if there are buildings the fief will of course cost money
- whether the fief is in a shire with special resources (indicated by extra symbols on the map), in which case it will be possible (when the fief reaches level five) to chose an option that produces the special resource in addition to the three kinds of food, wood and stone. One can then sell the special resource and earn extra income.

It is almost certainly a good deal to purchase the most expensive fief one can afford - 200 silver will purchase a fief with 250 silver worth of buildings, so one has saved 50 silver and regained much of the time one lost when not having a fief.