Ok, here's your answer...

"Here I Go Again ('87 Remix)" which is also sometimes sub listed as "USA Single Remix" or "Radio Version", depending on which album or single you have it on, is in fact the version the Dan Huff plays guitar on.

Even though it says "Remix", it is more a re-record, as it features entirely different musicians than are on the album version. This version is produced by Keith Olsen, and the musicians who play on it are...
David Coverdale : Vocals
Bill Cuomo : Keyboards, Keyboard Bass
Dann Huff : Guitar
Denny Carmassi : Drums
Tommy Funderbunk : Backing Vocals

...as opposed to the album version, which was produced by Mike Stone & Keith Olsen, and features these musicians on the track...
David Coverdale : Vocals
John Sykes : Guitar, vocals
Neil Murray : Bass
Aynsley Dunbar : Drums
Don Airey : Keyboards
Bill Cuomo : Keyboards
Adrian Vandenberg ; Guitar

As for "Give Me All Your Love" with Vivian Cambell, that version is also sub referred to as "Single Version", "1988 Remix" or just " '88 Remix". It's pretty much the same musicians as the album version, just with Vivian Cambell replacing John Sykes guitar solo with his own, and a little added keyboard from Bill Cuomo. It runs 3:15 as opposed to the album's 3:29.