Since you say you're a first-time DM, I might exceed the scope of your question slightly in my answer. You're up against a philosophical question: Are the players co-tellers of the story, or "passengers" in it? This affects whether or not a particular quality is a Pro or a Con.
Players as Co-Tellers
In this approach, you treat the players as storytellers, and your job as DM is to arbitrate disputes between them (like an editor working with multiple writers) and to provide a general framework for this to occur. You keep the 'grand vision' of the world, while they cooperatively tell stories within it.
- Pros of revealing backstory in this approach: The players are able to incorporate one-another's stories into their narrative plans, and can decide how to use their own characters' motivations to further the 'mole' narrative.
- Cons of revealing backstory in this approach: Minor, but if the other players don't like the narrative, they'll be well-equipped to bypass it.
Players as "passengers"
In this approach, you treat the players as mostly reactionary inhabitants of the narrative, rather than near-equal participants in crafting it. This more closely resembles the 'traditional' DM/player relationship, with the players and characters both being surprised by in-game events. It allows more authentic reactions on the part of the players, but can sometimes create tensions since the DM decides how the characters' arcs will unfold rather than the players getting to develop their own visions.
- Pros of revealing backstory in this approach: There really aren't any. It basically forces the players into the co-teller role, which might make your job as DM easier but ignores the whole point of this approach.
- Cons of revealing backstory in this approach: It ruins the surprise and authenticity of the players' reactions, and essentially forces them out of their characters' heads.
You are the DM, you can say No, although "No, but ..." also works
You are not required to change your world to accommodate a single player. What are the other players creating, as characters?
Saying yes to the android theme is workable
For the "android" theme, consider making the PC a construct; it is a creature type in D&D 5e. While it's a matter of homebrew, you can work on this together with your player using the Warforged1 from the Eberron UA as a starting point. This homebrew needs to be a collaborative effort; you get the final say since it needs to fit into your campaign world. (Perhaps a permanent curse/magical effect happened around the time of the character's birth?)
- Your player is an experienced DM; the work on this homebrew won't be a burden on you; that said, you need to do the final check on the homebrew to make it fit into your world so that it's not overpowered, nor unbalanced, compared to other PCs.
You two can have some fun creating this homebrew race. If you don't want to do the gunslinger class, then suggest to the player (perhaps) a hand-crossbow using character who takes the crossbow expert feat as your world's version of handguns.
CROSSBOW EXPERT
Thanks to extensive practice with the crossbow, you gain the following benefits:
- You ignore the loading quality of crossbows with which you are
proficient.
- Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
- When you use the Attack action and attack with a one handed weapon,
you can use a bonus action to attack with a hand crossbow you are
holding. (PHB p. 165, w/errata correction).
The "mafia" connection can be a trade guild, merchants' syndicate, a thieves' guild, a druid conclave working to roll back the overbuilding in certain areas, or a cult run by a Trickery cleric (or a Warlock) who is trying to slowly wrest power from a wizard's conclave. They sky is the limit regarding secretive and criminal organizations.
If you say "No guns" stick to your (no) guns ... :)
Your player appears to want to play in a different campaign than you are running. That happens sometimes. Ask him to create a character that fits your campaign. Your player's character needs to fit in with all of the other characters in the campaign that are being played by the other players. Making this a joint homebrew project can be rewarding for you both, and fun, as long as the party fits together well enough.
D&D 5e's basic model is that of a team of adventurers. Does this player want to be part of the team or not? You both need to clear that up before the adventures start. Likewise, he needs to discuss that with the other players.
"No, but..." becomes "no to the guns but yes to the android theme"
1 From the UA Eberron
Warforged
Although they are constructs, they have much in common with living creatures, including emotions and social bonds, and perhaps even souls.
Ability Score Increase. Your Strength and Constitution scores increase by 1.
Size. Medium.
Speed. Your base walking speed is 30 feet.
Composite Plating. Your construction incorporates wood and metal, granting you a +1 bonus to Armor Class.
Living Construct. Even though you were constructed, you are a living creature. You are immune to disease. You do not need to eat or breathe, but you can ingest food and drink if you wish. Instead of sleeping, you enter an inactive state for 4 hours each day. You do not dream in this state.
It's a good place to start. Also, since this answer was written, the Warforged become an officially published class in the Eberron: Rising from the Last War setting book.
Best Answer
Tasha's Cauldron of Everything has rules for sidekicks.
In the section on Sidekicks, we see:
It goes on to give detailed rules for each sidekick class. Speak with your DM about implementing these features for the character, choosing an appropriate sidekick archetype for the backup character's class, converting it to a proper player-character when you retire your previous character.
Note, these are optional features and it is entirely up to the DM to implement them or not.