Does The Last of Us disc version install to hard drive

Depending on the difficulty, you'll find more or less items during your quest for survival. The harder the difficulty, the less items you'll find. You'll still be able to find all collectibles regardless the difficulty you're playing on.

Not all items disappear on harder difficulties. Weapons, Skill Pills, Parts, Training Manuals, Comics and Artefacts can be gotten during any of your playthroughs.

The harder the difficulty, the more damage you take from enemy blows. Some enemy attacks retain their instant-kill effect on all difficulties. Enemies will also notice you considerably more quickly the harder the difficulty.

The Easy difficulty also has an additional option for 'Lock On Aiming', which makes it easier to shoot targets.

The Survivor difficulty doesn't have a Listen Mode nor Melee Prompts for in-game combat.

Source: Walkthrough by Absolute Steve

The money is gained by completing challenges. You should be able to find them under Bonuses -> Tags in the menu system. You collect money (amount of which varies with challenge it seems) for every challenge completed. Some of the challenges are associated with trophies, but the money you earn from that is not linked to any trophies, neither are the unlockables that you purchase with the money you've earned.