The ability Static Shield works very much like "Power Word: Shield" from World of Warcraft. For those who haven't, the ability simply blocks damage, all damage, until either its absorption limit is reached, or its duration expires.
Now, to answer your questions:
Is it a static number or is it influenced by my stats?
Static Shield seems to be affected by a percentage of your force healing bonus, as per my earlier comment.
Does it absorb all types of damage?
What about DOT's?
DoTs deal damage, hence, they are absorbed.
Does the shield cancel DOT's outright? Or only the ticks that fire while the shield is active?
If the shield is present when damage would be done to you, that damage is prevented and absorbed. So only ticks that, well, tick while you're under the buff will be prevented. Static Shield has no affect on the duration of debuffs.
Bonus Question: So what won't it do?
Static shield will only block the damage portion of abilities. Many stuns and interrupts (for example, Electrocute) deal damage in addition to their effect. While this damage will be prevented by the shield, the effect (sun, interrupt, etc) will not.