For instance, play group A, then play group B for second game in a back to back.
I can't confirm 100% but my best guess is no. First of all, it'd be tough to find 10 players who could all start on one team, and that a team would also be able to afford. The best example of someone doing something like this is the Greg Popovich coached Spurs, as on multiple occasions they will bench Manu Ginobili, Tony Parker, and Tim Duncan, along with others for the back end of back to back games, as a part of keeping them rested and healthy.
Another thing that would be tough in this situation is the roster size of an NBA team. You can currently have 12 active players for any given game, so if you had an entirely new starting 5 for the 2nd game of a back to back, you'd only have 7 total players you'd be able to play, unless you played some of the starters that are "resting", which would kind of defeat the purpose of resting them, and not just starting them in the first place.
Normally, when a team is going to play a back to back series, they will try and play their main players less than in a normal game, so if LeBron and the Cavs play a back to back, chances are, David Blatt will try and get LeBron off the court with 25+ minutes instead of his usual 35+ minutes to keep him somewhat fresh for the next game. Most of these NBA players are in good enough shape that a back to back isn't going to hurt them much anyway.
This doesn't really have a whole lot to do with the question, but I just read an article stating that Adam Silver, NBA's new commish, is looking to realign the divisions and make it so that teams don't have to travel as much, and keep back to backs at a minimum to reduce the stress on players overall.
No teams have had alternating units to my knowledge.
It makes more sense to rest your starters with the most minutes. It is easier to play 1/2 of 2 games than all of 1 game.
Spurs did not bring Tim Duncan, Tony Parker, Manu Ginobili or Danny Green to Miami one year. Last game of a 6 game road trip, an act in which the Spurs were fined.
Unless a player is listed as injured they must be present on the bench during games. The league must be notified in advance of any players that will be rested.
On some teams a starter will play with the second team to make practice more even. Pippen played with the second team to guard Jordan during their practices. When a game is looking to end in a blowout you would often see Pippen out there with the second team near the end of the game.