How do tier bonuses work

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.

No - crew bonuses do not stack - at all. In the instance two or more of your crew members have an ability that provides a crew bonus, these do not stack. However, there are a few caveats;

• Fast Learner (ace) provides a crew experience bonus, this is separate from Fast Learner (not ace) which provides a personal experience bonus. These two bonuses are separate bonuses, meaning if every member of your crew has one point in Fast Learner and one of your crew members has it aced, every crew member will receive a double experience bonus (a personal bonus from having one point in Fast Learner, and a crew bonus from the crew member that has it aced). If two or more crew members have Fast Learner aced, this bonus does not stack.

• Endurance (ace) provides a crew stamina bonus, this is separate from Endurance (not ace) which provides a personal stamina bonus. This works in the same way as Fast Learner.

• Abilities like Leadership (both ace and not aced) which provide crew bonuses at both levels do not stack. If multiple members of your crew have one of these abilities there is no additional bonus provided to the crew (they will, in the instance of Leadership, receive a 25% bonus for the first tier or a 50% bonus for aced Leadership)

This means, if you're building up a crew that is going to run heists together constantly, you'll want to avoid doubling up on abilities like Leadership but may want to each expend a point in abilities like Endurance or Fast Learner.