Imo, kicking, just like punching, doesn't absolutely NEED a target to hit. Sure, it helps to get the correct technique in (but only if you know what to look for), but if you manage to get the technique right, you don't need a target. The technique in striking is always relaxation and weight distribution.
People who do correct shadow boxing (ie. Cubans, Soviets, bare knuckle boxers from before the 1800s) have no trouble knocking trained fighters down, even though they don't use heavy bags or only use them very sparingly (and not very heavy at all). The "heavy bag" was once about 20 lbs and only became heavier during the last decades.
I can only speak of myself as an example, but I didn't need bag or mitt training to kick "through" Thai mitts or break rocks with my hands. Does it help? Sure, again, if you know what to look for. But it's not absolutely necessary. Also keep in mind that there are lots of boxers or Thai Boxers who really don't have any punching or kicking power in spite of using the bags and mitts, so it's not that easy. It's always about technique.
And to answer your other question: Snap kicks with pull back are down if you wear shoes (see: Le Savate). Follow through kicks are kicks you do when you don't wear shoes (see: Thais). Imo, snappy kicks with shoes hit A LOT harder than the follow through shin kicks.
EDIT: Typos