1 - Press F12, that opens Task Groups window. There select Special Orders / Organization tab. And finally click on Start Task Force Training button.
2 - Carrier should have more fuel, because it needs to refuel stationed fighters, you need magazines with missiles if you have missile fighters, if you have beam fighters, then you don't need any magazines. You can have Maintenance Storage Bay as your fighters will consume Maintenance Suplies to repair damage when they are docked. There also should be extra Crew Quarters on your carrier for fighter crews. You need to select Keep Excess Q checkbox in ship design screen to allow that.
This is small carrier I have in my current game:
Myth class Light Carrier 12 800 tons 247 Crew 2036 BP TCS 256 TH 1280 EM 1200
5000 km/s Armour 2-48 Shields 40-300 Sensors 1/1/0/0 Damage Control Rating 31 PPV 0
Maint Life 4.85 Years MSP 2094 AFR 119% IFR 1.7% 1YR 147 5YR 2208 Max Repair 160 MSP
Intended Deployment Time: 9 months Flight Crew Berths 12
Hangar Deck Capacity 2500 tons Magazine 500
Rolls-Royce MES-320 Magneto-plasma Drive (4) Power 320 Fuel Use 32% Signature 320 Exp 10%
Fuel Capacity 1 000 000 Litres Range 43.9 billion km (101 days at full power)
Theta R300/384 Shield Generator (10) Total Fuel Cost 160 Litres per hour (3 840 per day)
Phalanx-250 CIWS (2x8) Range 1000 km TS: 25000 km/s ROF 5 Base 50% To Hit
SS-4 Katana (125) Speed: 48 000 km/s End: 22.3m Range: 64.1m km WH: 9 Size: 4 TH: 320/192/96
TF/SPY-1 Area Surveillance Array (1) GPS 21600 Range 317.5m km Resolution 150
ECM 30
Strike Group
2x F-16R Raven Scout Speed: 12631 km/s Size: 3.8
10x F/A-18 Hawk Fighter Speed: 12631 km/s Size: 3.8
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
Maintenance Modules serve different purpose. ships equipped with Maintenance Modules are basically mobile Maintenance facilities and they need resources to maintain ships.