What are the factors that govern over the path that shrapnel and/or other particles follow upon explosion of explosives(the ones that are planted i.e. stationary ones) etc. Is it possible to predict the path of all the particles ? Also is it possible to make the particles move in desired directions ?
To predict the path of shrapnels one needs to perfectly know how the bomb is built i.e. how it will defragment. So it's theoretically possible but only if we're given the initial conditions.
As Sagnik pointed out what you know is that the total momentum will be conserved. So for a "stationary" bomb the total momentum will be 0, for fireworks the global motion of the shrapnels will be parabolic (if we neglect air resistance).
I think only one factor governs the path of shrapnels : Conservation of Momentum.
Even when the explosive is planted, the principle of conservation acts, for the total sum of displacement of shrapnels would then equal Zero. Thats why for a stationary explosive, shrapnels scatter in all directions.
It is not "impossible" to predict the path of all particles theoretically. Practically, unless we have a special explosive that defragments along certain parts I dont think its possible to keep account of so many shrapnels, for example : a real life grenade.
As pointed out in other answers, Conservation of Momentum will be the main and most important factor. However, that isn't the only factor.
Internal Pressure: The explosive may (and IRL will, to varying extents) generate uneven pressure. This may (and IRL will, to varying extents) dictate how other factors related to the acceleration of the shrapnel will apply.
External Pressure: In order to generate outwards acceleration, and explosion and/or shrapnel have to overcome whatever external force acts upon them. Shrapnel acceleration from an explosion in a vaccum will be different to one at atmospheric pressure, which will be different to one underwater, which will be different to one in dense magma.
Fragmentation: Shrapnel often includes or depends upon the fragmentation of the explosive's casing and/or of other fragmentaton elements. You'd need to know the design and material of these elements in order to understand and/or predict how the shrapnel will form, as shrapnel pieces of different shapes, masses and orientations will be accelerated differently upon the explosion, as well as later due to external resistance (assuming the explosion is not in vacuum).
Disregarding all of the factors other than CoM, the shrapnel's initial trajectory will be a vector of whatever momentum was present before the explosion, plus whatever momentum is accquired from the explosion.