As a rough rule of thumb, every 750 affection is worth roughly a 1% reduction in completion time on crew skill tasks.
Edit: Comments indicate that the first 450 points of companion affection are worth 2% off the top, and that further affection follows the 1%/750 formula. I haven't seen the exact data set, but this does fit the patterns I've seen closely enough to be plausible.
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?
Yes.
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.
Best Answer
No, there are not enough conversation options. I've just started maxing her myself. I don't think four types of gifts are particularly few, though.
However, you might be able to raise her affection through repeatable quests. Several of the Belsavis dailies have choices that affect companion affection, for example. But it will be slow!