First order you get is to join with your team:
How do you join up with your collegues ?
Just press the '4' button on your keyboard, after you have been asked to join up. This is the command: autopilot join formation and you should be off.

How not to fail the mission ?
Shoot as many targets as possible so your collegues don't get every plane down, if they shoot more targets than you, mission failed.

Don't forget to face the target and press 'T' so your laser can lock on. In the second part of this mission your missiles will be activated, so you'll need a lock on.

Fly to warpgate on your own:
How to do it the easy way without having to go trough the debris field and crashing on rocks:
As soon as the mission starts, so you don't have much time.
Point your Figher's nose towars your collegue Willians lock on to him and press the '2' key on your keyboard, this will activate the auto-pilot and will engage your ship in following your collegue up to the warpgate. Sit back and wait till your ship is delivered up to where you need it to be.

At the warpgate:
just fly trough the 'circle' = 'warpgate', it will automatically take you to your next mission.

After the warpgate and up to your next mission:
Just press the '4' button on your keyboard, after you have been asked to join up. This is the command: autopilot join formation and you should be at next traning site.

Attacking ground targets:
Keep throttle at around 60%, save after every attacked ground target.
You don't need to lock-on to ground targets, keep your nose towards the ground targets.
Use the laser cannon to fire at the ground targets, the laser will lock-on to then, even when you dont allign perfectly with the ground targets. Your crosshair does not have to be over the ground target to hit it with your laser.

It's not sniping ground targets, your laser will correct a misalignment.

In this mission you are going to have to fight of enemy's. Most of them will be taken out by allies.
Once they have taken care of, select the CTV Ship and dock with autopilot or '3', dock with target.

Follow your allies (auto-pilot) until you reach the enemy ship.
Wait until they blow a hole in the entrance of the ship.
Fly slowely trough the hole until you reach the giant blue ball (core).
Change your view with the 'V' button, till you have the outside view of the ship, where you can select the logbook, to read the logbook.
Next to the logbook icon (lower right corner of your screen), click on the 'exit-like' icon, this will drop the bomb. Exit as soon as possible before the bomb detonates.

In-game mission number 11, part 3.
Don't fire the laser weapon but the gun that fires physical projectiles. Durandalle shield is only good against energy based weapons. Try to get close enough (less than 2 km for a good shot).
Source

In-game mission number 33, part 2.
There is a time limit on this mission, so work as quickly as possible.
Fire the rockets towards the missile ships, but only aim at one of the 4 fuel tanks. These break easily and explode quickly.
2-3 rockets and some gunfire should be enough to break one of the four fuel tanks, making the ship explode.