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.
As far as I know, there are no prerequisites for pro jobs (I saw them from the lowest reputation levels). The difference in comparison to normal jobs is that you cannot try the mission again if you fail. You get one try and that's it.
Another thing that makes pro jobs special is that there are no pro jobs on normal difficulty. They are always on hard, very hard or overkill.
Best Answer
Every silencer is totally silent. "Threat" is essentially the new "noise" stat, and for all silencers, the "threat" drops to zero. The main differences between the different silencers come in their damage and concealability penalties.
There are a number of ways to do things more quietly though. The Shinobi ace causes guards to make 95% less noise when killed by melee or a silenced weapon. Also remember that for most guards, your melee strike will take them out in one (maybe two) smacks, and is even quieter. Careful not to get cuffed though!
At the end of the day, stealth comes down to practice. Sure the right equipment and the right build helps a lot, but at the end of the day, even with the best equipment and skills, it's still very easy to mess something up. And you have a very small margin of error with stealth, depending on the mission.