A1 dribbles across midcourt full speed trips on his own feet fumbles the ball and then gains control of the ball on his way down and slides about ten feet. Never rolls when he slides, just slides. Travel or No?

Ahhh, what the heck, Travel!

If he's holding the ball when anything other than his feet or hands touch the floor, it's traveling.

If he has control of the ball before he goes down it's a travel. Perhaps you'd be more interested in this question: A1 dives for loose ball, slides, grabs the loose ball while continuing the slide. Now whatcha got? ;)

nothing as of yet! what does he do next?

player fumbles the ball as he is going down do you still have a travel?

If a player dives for a loose ball controls it while sliding you have nothing unless the player rolls or sits up. If the player rolls or sits up advantage is gained and that is where you have a travel.

Not correct.

If the roll is part of the momentum of the slide it's still not a travel, and a player on their back may sit up.

how can you let a player gain advantage through sitting up?

It's the rule -- if the player is on his/her back s/he may sit up.

See NFHS case book play 4.44.5SitB.