You can fire your interpreters and any extra interpreter you may have after a successful FOB mission.
From a handful of FOB invasions of my own, I haven't once found a better interpreter than the ones I already have. In fact, the interpreters were all exactly identical to mine, from name to stats. I therefore assume that there isn't any way to improve your interpreter staff.
However, you do not need to keep your interpreters in Mother Base. As long as they've been assigned to your Support team at least once, you can make use of their interpreter skill even if they're no longer in your base (Thanks @user2357112 for this). Once fired, there is no way to get them back, other than extracting one during an FOB invasion. The only exception being Afrikaans interpreter, one of which can be extracted as many times as necessary by replaying mission 16:
Specialists are easy to replace. They are found during main missions, and are usually special elimination targets or prisoners. Which specialist you get during which mission, is specified at the top of your iDroid map as you select the mission.
Before you start replaying any of your early missions to get better specialists, however, I'd recommend you take a good look at the repeat missions. Those are exact duplicates of earlier missions, but have restrictions placed on top. These missions usually award you with significantly better staff than their original.
For instance, the mission
Over the Fence awards you with a Bionics specialist (your main extraction target), who is an R&D specialist ranked somewhere between C and A. However, the
[Total Stealth] Over the Fence mission can easily award you the same specialist with an A++ or S rank instead.
Keep in mind that the specialists aren't always found at the same location, or found at all. Special extraction targets, like the Bionics specialist in
Over the Fence or the arms dealer specialized in Missile Guidance in
The War Economy, are guaranteed to always be the same target, however random prisoners aren't guaranteed to always be the specialist you're looking for.
For instance, during the
Backup, Back Down mission, I found my Drugs specialist in the Wakh Sind Barracks. While playing the
[Extreme] Backup, Back Down mission, I expected the Drugs specialist to be where I found her the last time. And although I did find her exactly where I expected her to be, she wasn't a Drugs specialist this time around. In fact, none of the 6 prisoners I extracted were Drugs specialists. So you may need to replay the same mission several times before you can find the specialist you're looking for.
As for the Legendary Gunsmith (Master Gunsmith), you can give him the same treatment as your interpreters. You can still customize your weapons even if he's no longer at Mother Base.