From Experience:

I have players playing evil characters, both now and in the past, and I've played an evil character a few times as well, like every time I've ever played a Drow. (That's right, those characters were enforcing the stereotype from the monster manual!)

When I discover the player wants to play an evil character, I give them a simple choice:

Your evil character's motivations must work with the rest of the party OR you don't get to play an evil character.

If your character oversteps bounds or decides to run counter to the party's efforts, they will become an NPC, and you will need a new character.

That's the deal, and part of the social contract at my tables.

Here is some good advice- successful evil characters need good motivations, have a good goal, but are not adverse to using the wrong methods. They need to be valuable enough to the party that the party can look the other way.

• How to play an evil character in a RPG
• How To Play A Good Evil Character

Moustache-twirlingly evil characters is most easily solved by direct talking about it with the group. Is this play fun? Is this what we want? Can the evil character scale back the evil-for-evil's sake and get a goal or something to work towards, or know that those evil actions have consequences?

^{_{I'm also surprised that no characters (and therefore players) have indicated that (1) this is terrible, (2) how long will it be until he turns on us, and (3) their adventurers are out to kill monsters like this...}}

An Ounce of Prevention:

For those starting or about to start a table, the same page tool, or anything of its kind, can avoid this kind of thing. Even a simple statement at the start of session #1 could help.

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:

1. You ignore the loading quality of crossbows with which you are proficient.
2. Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
3. 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.