2 questions
 

1. High School- During a dead ball situation (timeout). Can an intentional base on balls be awarded during the timeout?
2. After a batted ball, batter unintentionally throws the bat and goes right between me (U1) and the catcher. Next at bat for the bat slinger, same thing. This time it gets me in the shin guards. I call time and issue a warning.
My question is, if it happened a 3rd time, the rule book states under 3-1-c (carelessly throwing a bat) ".....and the next offender on that team shall be ejected". Is the offender called out, then ejected? Restricted to the bench?
Thank you

Yes. In fact, time must be out to award the intentional walk.

Ejection only. Not an out. The runner is replaced.

Be careful ejecting a player who's throwing a bat after they swing, hit the ball, and run...versus the batter who throws his bat like a flippin' boomerang after you ring him up...I think you need to judge the sportsmanship aspect of throwing his bat...

Nope: not on this one.
Careless: warn and eject for further violations.

That said, I have previously been in something of a pi$$ing match with a certain well-known internet umpire guru for my comment that I have never SEEN a "careless" toss of a bat by HS-age players: many careFUL throws, amid a number of clearly INTENTIONAL throws, some of which were quite dangerous, and not a few of them angry or even malicious: different rule for those.

Not under FED.