If anything, defending against droids should be easier than against a living person. Instead of needing to sort out the complex web of emotions of a living being, you're just detecting the timing of the basic, thoughtless routines of programming. As Han said in A New Hope, "Good against remotes is one thing, good against the living? That's something else"
Precog is precog. Qui-Gon Jinn made it clear in TPM that Force users sense events before they happen, making them appear to have remarkable reflexes. This has been basic Star Wars understanding since 1977. Mark Hamill wasn't moving at superhuman speeds when he defended against the training remote on the Falcon. His blade was in position before the small droid had even fired its shots.
Yeah, precog isn't wholly dependent on reading the minds/thoughts/motives of living beings or whatever. It just gives you brief glimpses of the future in general.
The best canon example is when Vader used his precog(or "double vision" as he called it) to pilot a Star Destroyer through chaos of the Unknown Regions while traveling through hyperspace. His precog enabled him to foresee what random planetary debris would be in his flight path, and he successfully maneuvered around it whilst moving at FTL speeds.
There were no "intentions" to be sensed. Vader just... Glimpsed the future, and acted accordingly.
There still has to be some level of speed involved though, precog doesn't mean a whole lot if you're not quick enough to act upon it. Well against multiple shooters or multiple bolts, if it's something like Luke and the training remote, sure you don't need to be ridiculously quick.
Agree. When dealing with multiple shooters(or rapid blaster fire), enhanced speed/reflexes would have to be part of the equation as well. Like you said: knowing where the bolt(s) are going to connect means nothing if you are unable to react fast enough to deflect them.