If your soldier gets gravely wounded in a mission, there is a chance that the soldier gets shaken. This chance is 20/25/25/30% for the four difficulties.
What is gravely wounded? It means that the recovery time is more than 168 Hours (336 on Legendary) - this is determined at the end of the mission.
How is recovery time determined? Based on the lowest HP percentage at any point in the mission, a number is generated within certain limits. There are four "buckets": up to 20%, 21-50%, 51-75%, 76+%.
Example, your Soldier has 10 HP and takes 6 Damage, which brings him down to 40% health. At the end of the mission, the game looks in the 21-50% bucket to see the range of how long recovery takes and picks a random number from that. If that random number is more than 168 hours (336 on legendary), you're gravely wounded and the game rolls if you're shaken.
Note that the source of damage doesn't play into it, and neither does healing. The game records the lowest your HP ever was. E.g., 10 health, take 6 damage, heal 4 damage, take 3 more damage, heal 4 damage -> Even though you end the mission with 9 HP, the game records that you were down to 4 HP, which is 40% of 10. That percentage is the ONLY thing that counts.
I do note that the spread between best and worst recover time is MASSIVE. For example, a single point of damage (the 76%+ bucket) on Rookie difficulty puts your Soldier out of commission for 5 to 25 days - completely random.
For more technical details, I dug into the source code here.
Bonus Answer: If you recover from being shaken, you get a permanent increase to Will (4 to 13 points) and can't be shaken again - it's like Vaccination.
In order to gain Intel you can scan at your HQ, but you must ensure that you have the 'Gain Intel' perk selected at your base.
When you arrive at your base, on the left hand side of the map marker is a fist icon, click this and then spend 25 supplies to change to the 'Gather Intel' perk, and then when scanning you will gain Intel.
The other perks I've seen so far are 'Quick Building' and 'Heal Faster'.
Best Answer
You can get one extra faction soldier from the first resistance faction that you contact by using a covert action that requires high influence in that faction.
With the WotC tutorial on you always encounter the Reaper faction first making it only possible to get an extra Reaper.
I read this in another thread that said that a dev had said it during a livestream and it seemed correct my first full run of the game so I believe it to be true but if you find proof otherwise, please tell me.