I understand that the design of the original corvette is due to role-play, but in my opinion the ad-hoc "emergency" redesign and frigate need rework to be better military ships and doing so would still be RP friendly.
Both are too slow (especially for beam ships!), and imo one of the meta responses to a faster alien ship would be designs with more speed first of all, even at a cost of other systems. Similarly, both ad-hocs are still designed with too much spare fuel and maintenance life, drop those significantly and add either additional engines or a newer faster engine design (at least for the frigate, it's a new ship entirely so RP-wise it works). If you need to forward-deploy them send along a tanker and/or maintenance ship or set up a maintenance base somewhere (right now a base because in 1.9.5 pure ship-based maintenance modules don't work yet). Pure military ships shouldn't waste fuel and MSP on "patrol" unless it's just for RP, like the first ship.
Every ton counts in small ships, I wouldn't have much more than enough engineering/deployment/fuel than just enough to get to the aliens, fight, and get back to base with a bit to spare. (On a lot of my early designs the "getting back" is a bit... optional - they knew what they were getting into when they signed up - and I'll maybe tanker/tug any survivors home but that's dependent on the game RP).
Make sure you do keep enough MSP buffer to at least 2 times maxrepair to fix a destroyed system from battle, but honestly with small ships if you're getting significant internal damage you'd probably lose the ship anyway most times. Ah, but hope springs eternal, etc. so why not.
Similarly you can also drop some armor too, small ships either need a lot of layers to survive, or (mostly) won't so why not use that space for better things ?
The frigate has kind of an awkward layout of gauss turret AND a CIWS. I'm not sure I see the point of that, gauss turrets are always more effective than CIWS ton for ton because they can protect more than one ship. CIWS is only to protect a commercial ship without it becoming a military one. The only good thing about it is that it still works during jump shock, I think, but still it's pretty inefficient and you can't afford that.
Also there's no real need to have gauss ranges more than minimum (10k) for missile defense, and if you need to use them to attack ships you'll have to be much faster than them anyway so point blank ranges are still fine (though in your case you'd prefer to use railguns for antiship weapons like in the corvettes). You'll want to have a longer-ranged BFC if you can though for accuracy's sake.
The turrets should also be redesigned to match the max 4x BFC speed which they don't seem to be.
There's no res1 missile active sensors, you need to add at least a size 1, 1HS resolution, active sensor to the designs for small ship and missile detection - even if you've got other ones on other ships in the fleet, a small sensor like that only takes up 50 tons and provides cheap redundancy and is worth it. At beam ranges it'll still work fine (unless the enemy missile speed x 5 is greater than the sensor's range, if it is make the sensor larger).
Once you've rejiggered the designs as above add more weapons if you can to the space saved, otherwise add fuel until it's the size you want.
Tl;dr: for the two later ships reduce "deployment" fuel and maintenance (and maybe armor), add more speed, then additional sensors and weapons, in that order. For the first ship, eh, add the 1res sensor but it's RP so do what you want.
