What, if anything, can I do with the “progessive” man in the Lansdowne Residence

To add to the other answers, Elizabeth will occasionally give you Salts. More details behind that as mentioned in the answer(s) to this question: How does Elizabeth getting various loot and then giving it to you work?

Also, from the BioShock wiki, "Salts" article:

...certain beverages such as coffee and soda will also replenish a small portion of the player's Salts, while drinking alcohol will consume a small amount. Smoking cigarettes will also increase the player's Salts, though at a cost to their health.

Watch out for Salt Machines that will refill 100% of your Salts, free of charge and can be used repeatedly:

Despite promises to the contrary, "1999 mode" is more like one difficulty notch above Hard.

The things that are the same:

• The plot/story/dialog is identical.
• Fixed spawns are identical, you'll find the same weapons, ammo, gear boxes (although the gear is randomized in every difficulty), infusions, etc.
• Enemies spawn in the same locations, in roughly the same quantity as before. The harder enemies are definitely the same, although the weaker ones are a bit too numerous to be compared easily.
• The weapon and Vigor upgrades are identical and cost the same amount of money. I haven't noticed a large difference in my money supply. Any suggestion of "combat specializations" that must be tuned is puzzling.

The things that are different:

• Checkpoints are similarly spaced, although I've been told there are extra ones before the Handymen (the really hard "boss" level enemies in the game).
• You still get a shield, but it takes fewer hits and recharges much, much slower.
• It takes more shots to down an enemy, but bullets are somewhat more scarce. This makes weapon upgrades slightly more important, but I honestly have had very few situations where I ran low on ammo, and with your "companion" handing you weapons, it doesn't seem like a big deal, honestly.
• In lower difficulty levels, you can get a "hint" in the form of an arrow pointing towards your objective by pressing a button. This "navigational aid" is disabled in 1999 Mode
• If you die and don't have enough money, you will not be revived. You'll have to restart from a checkpoint. (Although, given the high demands on your funds, I'd suggest restarting from checkpoint if you die regardless)
• You can't adjust the difficulty from the menu. This isn't that much of a problem unless you plan to go after some achievements after beating 1999 mode that would have been trivial on lower difficulties - you'll either have to endure 1999 mode for them, or start over from the beginning on another difficulty.

Overall, it's very similar to other FPS games on their hardest difficulty. I'm doing pretty much the same things here that I would in a Legendary run of a Halo game, or a Veteran run of a CoD game.

You can unlock it with the Konami code at the title screen, or by finishing the game on any other difficulty level. Many games have this feature of locking out the hardest difficulty until you've finished the game, and I would highly suggest you take this route. There are times when you will want to know the lay of the land in a situation where you can screw up and still survive. Knowing what weapons to upgrade is harder without knowing what weapons you'll encounter, for instance.