First of all, I'd advise going for a DEX of 14 and a WIS of 18. While dexterity is important, as a mystic maxing your wisdom score really does a lot more for you. Remember your resolve points are tied to Wisdom, and you want a lot of those.
Beyond that- long arm proficiency is a solid feat, as you said. Sure, you won't be as good as a soldier, but you can still be a lot better than "a mystic with a pistol". I also strongly recommend picking up spell focus. Increasing your spell DC's is always useful. It's available starting at level 3. However, you won't be able to get both specialization in long arms and spell focus at 3rd level, so you'll have to decide.
Spell selection wise, I have a few favorites:
Daze: (Denying an an enemy an action is always good. Don't take if you don't expect to fight humanoids at all)
Stabilize: I agree in combat healing isn't good. But this can not infrequently be the difference between "a party member spends 3 resolve points to stabilize b
Vs "saving the points to regain stamina". Or between "not dying" and "dying".
Whisp Ally: Either make an enemy attack less effectively, or give your allies a better chance to hit an enemy. No save, no spell resistance.
Command: I've found this useful for getting ranged enemies to run right out of cover. Considering how prominent ranged combat is in Starfinder, I can see this getting a lot of use. Even against enemies in melee with a melee character in your party- make them drop prone and completely ruin their day.
In general, I've found that Mystics work best as debuffers and controlling the battlefield (either with terrain alteration/ summons).
First of all, I'd advise going for a DEX of 14 and a WIS of 18. While dexterity is important, as a mystic maxing your wisdom score really does a lot more for you. Remember your resolve points are tied to Wisdom, and you want a lot of those.
He's planning to be the party's pilot. If space combat will be reasonably frequent, a higher DEX might be worth it, combined with the other advantages it gives in combat. Also depending on the level the campaign goes to. They're already starting at 3. If most of the campaign is played at levels 5-9, then it's probably smart not to start with an 18.
And yes, unless you expect this to be a combat-light campaign, take Longarms, especially if you're going 16 DEX. But even if you're not.
Drow don't get a WIS bonus, but they do get a DEX bonus, so I've decided to pick Ace Pilot as my theme and Star Shaman for my Connection.
That's a non-sequitur though. Nothing necessarily wrong with those picks, but having +2 DEX or +2 WIS has nothing to do with whether you should have 16/16 or 18/14 in your stats.
I'm hoping that CON penalty won't be as painful as it would be in Pathfinder.
It won't be. A negative CON mod reduced a Cleric's HP by somewhere between 12.5% and 20% depending on level. Here it reduces your combined Stamina + HP pool by about 8%.
Yes, healing in combat is weak, but be very aware that there will be many times that hp getting hit will happen. So have plans for that, cause players get hit a lot in this game and gone are the days of rocket tag. Depending on spells selected Spell focus would be more valuable than weapon specialization. But yeah, Dex 16 Wis 16 makes a strong Mystic, and with that spread picking up longarms isn't a bad idea.
In the event you're shooting and feel like you're not hitting anything, remember you could always lay down Harrying Fire/cover fire/a to give allies advantages if you're struggling to hit an enemy with an AC higher than 15.
How many players are going to be in your party? Do they have classes and starship roles picked out? This info can help other's look for roles you can fill in. There are a lot of ways to build a character, but mystic is one of the classes that has fewer choices once you've picked you connection aside from spell selection, but it may be very dependent on who's in the party. For instance, if you have a technomancer in your party the you may want to focus more on healing and buffing. If not you may want to take some of the utility spells that would not be a mystics first choice but will help round out a party if you are the only caster.
Well I would like to caution you not to think of yourself as a full caster. The spellcasting classes in starfinder are closer to a magus or bard in a lot of ways. You should definitely put some thought into what you will be doing in combat on rounds when you are not casting. Longarms are a good choice for feats, but not the only choice.
If you have a solarian he will probably be your party's face as long as no one else really wants that role. With your high dex and wisdom you could do a couple of things for your non combat skills. It would likey be a good idea for you to have maxed mysticism at the very least since no other caster. Also consider stealth. I think it fits well with the drow race and keys off of one of your good attributes. Plus you'll have likely the highest perception in a group which means you're a natural choice for a scout. Survival is a skill you would be too dog for and I don't think is a likely pick for anyone else. Idk if your doing the AP or not or how prevalent tracking will be but it could come in handy. Maxed pilot ranks makes you a great pilot or gunner, so you can switch if needed.
Melee is not a good place for you to be, but you should still grab an operative weapon of some kind.
The biggest choices I think will be in spells. What kind of campaign are you doing? Is it mostly a dungeon crawal, or will there be a lot of chances to solve problems without fighting? Is it going to be mostly a murderhobo extravaganza or will there be more sudelty? Not saying ones better than the other, but it would make a big difference in what you should pick for your spell list.