A parabolic action is where a rod bends through a more or less even arc, as opposed to a rod where the tip section bends more than the rest of the rod. A paramedic rod, well I guess that stops heart attacks and things
Inchikus are one type of slow jig, there are butterfly jigs, madai jigs etc that all fall under that umbrella. A good salesman would sell you a different rod for every type but you will get by with any soft bait rod, some will be better than others of course.
I use Jitterbugs at the moment because they are reasonably cheap and work well but I've used cheaper ones and they work well too. The cheapies tend to have much heavier hooks that don't set as well but on the other hand fine wire hooks that the more expensive brands have need careful application of the drag setting! In other words take it easy or you will straighten the hooks.
I haven't tried Kaveman's jigs but the feedback here implies they are very effective.