Edit: WALL OF TEXT
Let me answer both questions here. CGs can be completed so long as you are playing. It makes no difference if you're in Open, Private Group, or Solo. Your progress is added to the total on the server. Once the CG's timer is up or the final Tier is hit the CG will end and rewards will be waiting at the station the CG was started at. Simply wait and collect at the Missions menu when docked. The Engineers are a whole other beast. Each has 3 main requirements and each is different. You might find yourself just cruising along blasting Wanted pilots Port and Starboard when suddenly you meet a ship that's relatively equal to yourself but sends you into a smoking hole of rage and despair. However, once you've started making a name for yourself, feeling confident about a ship and your abilities, and find that you love a ship despite any downfalls with maxed out Internals. That's the time to start engineering. An Asp Explorer setup for combat can be a rather formidable opponent. With Engineering though, those two medium Beam Lasers can increase a friendly's shield regeneration and those 4 small Gimballed Multicannons are now firing corrosive rounds that increase in damage as they inflict hull damage while firing more ammunition than previously imagined with Rapid Fire.
Engineering takes time. Lots of time. Having a small ship dedicated planetary landing can help finding materials such as Iron and Silver and a decent Wake Scanner can let you find unusual Wakes from other ships as they jump in and out of a location. The Sidewinder makes a great candidate for such a ship. It's small but having 2 Size 2 slots let's you carry the smallest Planetary Vehicle Hanger and with 2 Utility slots you can mount a low end Wake Scanner. At the start of the game, you can get a headstart. Find a big ship, target it, and let your ship scan it. If a noise pops up suddenly and a blue message appears above the center of your screen. You found a new material or unusual Data. The Cargo Scoop on every ship will let you grab junk that's floating in space while flying under 40 m/s (provided the object is targeted and in the Cargo Scoop's sights).
When you've upgraded a ship's Core Internals to A-rated (Life Support and Sensors can be left at D-ratings for increased Jump Range), and love the ship, that is the point you start Engineering. If you sit down into a Viper Mk.3 and love the rush of having a vessel that can fly faster than it has any real right to with A-rated Thrusters, Frame Shift Drive, Power Plant, and Power Distributor and feel no need to sell it. Keep it stashed at a station and find out what an Engineer needs to meet with you. You'll have 5 Engineers to start with and each needs something from you. One requires you to have 50 market contacts (sell at 50 different stations) then demands 200 tons of Gold once the invite is sent (most Engineers can only be met after you've built up Reputation with a previous Engineer). This is why having multiple ships is so important. Sure, keep your Viper Mk3 but that Type-6 that's being offered will come in handy. But NEVER LOSE FOCUS! Sure you'll have an apocalyptic laundry list of things to do but it isn't going to hurt if you don't get that Permit to Sirius this week. You have other things that need done. Run out into the darkness of the galaxy and live to tell the tale! Meet up with strange people and drill a 5 parsec hole through their engines, laughing at their torment as you collect a paycheck.
Also, Something that hasn't been mentioned: Crafting. Need a boost to your FSD range? Craft a Boost! Need more ammo? Craft a reload! Need SRV fuel? Craft some fuel! The materials you'll collect on your journey will let you make some amazing things that just might get you out of a bad situation (or turn a great situation into a nightmare for your target. Damage boost anyone?) Each item requires different things but those items will deplete your Materials and thus might prevent you from getting that Grade 5 Sensor mod you've been drooling over for the past month. Fear not though. Crafting does come in handy but won't come in too often to hamper your Modding.