0.3 seconds left — Would a dunk from a throw-in or off. rebound of FT miss count?
 

The rule is that if play is resumed with a throw-in or free throw and three-tenths of a second or less remains on the clock, then the only kinds of tries that would count would be a tap at the goal. But what if it was a dunk? Would that be considered a catch-and-release or a tap?

Catch. No basket.

Interestingly enough, the NBA has guidelines for these type of plays that basically says that a dunk can be counted if the ball is immediately adjacent to the basket. If the ball is not immediately next to the basket and the player has to control it at all, then there must be at least .3 on the clock to count it (as opposed to .4 for NFHS). They also wouldn't be able to go to instant replay to view this type of play (if under .3 seconds)

This has been done in an NBA game semi recently by a New York Knick player.

.4 on the clock
 

I had a game last week using NFHS rules with .4 on the clock.
On the inbounds pass, the receiver catches the ball just after elevating at the free throw line. He floats about 10 feet through the air while controlling the ball in the hand and then shoots all before the horn goes off. I didn't allow as I felt the clock did not start on time and that's the only way the ball could've been in his hands so long.
Partner said I was wrong to wave it off because with .4 a player is allowed to catch and shoot.

I'm with you.

0.3 for catch and shoot is for an immediate catch and and immediate shoot. If they hold the ball any length of time between the catch and shoot, it is going to take a lot more than 0.3 to complete the action. No shot.

The next J..MJ or Doc? or Peter Pan?
 

Do you by chance remember this high school players name that can elevate, catch a pass, and then float 10' through the air?

Heck, I might be able to float 10'. 10' really isn't that impressive. I'd hope that 95% of the players on the average HS team could jump 10'....and probably 15' feet or more for many of them.