So far, from what I could read online (in this guide and on the wikia, among other sources):
Briefing screen
Pay grade
The pay grade for a mission indicates how much cash players can expect to get out of a mission -- source.
Also this thread suggests it can go up to 10 stars.
Day rate
The dayly income rate is a cash reward with a multiplier for the day a heist takes (e.g. 1x in The Bank Heists and 3x in the Rats Heist) -- source.
Contract pay
The contract payment is a flat amount of cash reward based on the number of white stars (pay grade) -- source.
Payday
The overall payday is the sum of the other two cash rewards (pay grade and contract pay) and will be shown on the map if you select a heist -- source.
Yellow bonuses
These bonuses come directly from the difficulty (or "risk") of the mission, pictured by the yellow skulls on this very same screen. Normal = no skull -- overkill = 3 skulls.
Debriefing screen
Instant cash and bag loot items
The instant cash it the one you loot and put in your pockets directly during the game (jewels, cash bundles, ...) The bags are those heavy packs of money, jewels or even drug you'll have to carry in order to achieve a mission.
Balance
This section contains the sum of all the amounts contained in the Income section ($332,400 in the example given in the question) distributed between two type of accounts: the offshore account and the spending cash.
Offshore account
The offshore account consist of most of the money players steal during the course of their heisting career.
The player has no way of interacting with their offshore account and is only used to show off how much the player has stolen -- source.
Since August 30 2013, you can use your offshore account to directly buy specific missions from Crime.net.
Spending cash
The cash you get, finally. In the given example, it's 10% of the total amount, but so far I couldn't find any precise calculation to know if that percentage can vary or not.
This is the offshore account money and 10% of that becomes you spendable cash. -- source.
While there are currently no exact numbers on what causes an escape missions, I've noticed the following by observing when we get escape missions after completing the main segment of the mission:
- If no alarms are ever set off, there is no escape
- If you have the Expert Driver asset, there is no escape
- If you leave during an assault, there seems to be a very high (practically guaranteed) chance of an escape
- If you leave after an assault, before the next assault, there seems to be a reduced chance of escape
- If you leave after killing all enemies in a wave, outside of an assault phase, there seems to be a reduced chance of an escape
- Once you have set off an alarm, killing civilians will increase the chance of an escape mission
Ultimately, escape missions are there to prevent the "quick and dirty grind" - if you want to go in loud and don't prepare properly, expect an escape to happen.
Best Answer
I suppose there is one true statistic to this, but it is going to depend on your skill. I would do the following:
On this Steam Post, which I agree with, many players say to do the Shadow Raid. The thing is, you need 4 people that you can coordinate with (something public matches don't really allow).
I've never tried this tactic, but from the sounds of it and this video, you play on the hardest difficulty (Deathwish for console versions, or One Down if you can handle it), go loud, and have your ECMs at the ready. Kill anyone you run into, and place an ECM when needed to prevent the 1 minute remaining alarm. You'll earn around ~$13 million each time in about 5 minutes.
For Solo games here are some options:
Mallcrasher Overkill or Deathwish.
For this mission, you'll want a saw to be able to break into all the ATMs quickly. You'll need an ammo bag as well to replenish saw blades. You can cause the 50,000 dollars of damage pretty fast with a few well placed grenades to end the mission. There is also a jewelry store which you can loot for some more money.
Hoxton Breakout Overkill. This one gives a nice payout at the end, though it's not very fast as it is a 2 day job.
The Pro job version also grants more money, but obviously carries the risk of not being able to restart.I don't recommend doing this one on Deathwish or higher as it can be pretty difficult soloing.The Diamond Store on Deathwish or One Down. You'll want to take a "Control Freak" route, and use ECMs. This can be pretty profitable and fast. You may be even able to stealth it fast if done carefully enough by controlling the crowds and taking out the Guards.