I have 2 questions

The divisions are basically leaderboards by region and category, so you can lookup your rankings for your city, state, and/or country by weapon type, class/kit, or vehicle. Basically if you wanted to see who the best person with sniper rifles in Battlefield
Hardline in your city is, you would be able to with the division leaderboards. And the "Division Upgrade" alert is basically saying that you're moving up the leaderboards for that particular divison/category.

As for the cash in Battlefield Hardline, its similar to experience or score in previous Battlefield games. Previously you would earn experience based on your score and once you attained a certain amount you would unlock specific gear. Now with Hardline
you can actually progress in a much more flexible manner since you can choose which gear to unlock like weapons, mods, gadgets, etc, by simply purchasing which items you prefer.

So the answer to your question is the same as it would be in previous Battlefields: the best way to progress is to get a good score. Battlefield has always rewarded cooperative play the most, so if you want more cash be sure to work objectives and work with
your teammates. If you're an Operator, throw down some medkits and use your revive gadget. If you're a Mechanic, use the repair tool to repair teammates vehicles. And if you're playing Heist or Blood Money, work the objectives! Don't treat it like a simple
Team Deathmatch and just go for K/D, you'll earn far less cash that way. Also, you get bonus cash/score for doing these cooperative things with your squadmates not just your teammates. For example, a teammate heal is worth 10 points while a squadmate heal
is 15 points. In general, these squad bonuses are worth about 150% of what regular teammate bonuses are, so expect similar boosts across the board for all cooperative activities.

Here's some more info on earning cash in Hardline:
www.battlefield.com/.../how-to-earn-and-spend-your-cash-in-hardline

i believe the console is covered for 1 year and only covered for 3 years for rrod if you have had rrod before hand, however if you have only recently brought your elite brand new you shouldnt really have any problems.

if they cant fix your console they will replace it with the same type of system you sent them (in your case an elite)

^^^the above post^^^

suggested answer

Unless they run out of Elites, as that system is no longer being manufactured, so it is simply a waiting game. If it does break, hopefully before they run out of Elites.

Depends on the items. A lot of the item are account specific and if stored in the vault will be there for other characters.