SoCal

Yes, you'll be outside security after you go through Immigration, get your bags (shop at the duty free store, if you like, even upon arriving, not just departing, on international flights), go through Customs, then go upstairs with your bags to check-in for your TAM flight. You'll go through security for domestic flights, and won't likely have access to any lounges, unless you find one, such as the American Express Centurion Club, outside security (it's down the hall from the Luxor Hotel in Terminal 1; TAM's in Terminal 2). Food court outside security in Terminal 1 is okay but overpriced. We found the restaurant in the Luxor Hotel (next to the food court) better. Or just go to your gate and grab a coffee or such in that area. Can't recall where there are WiFi hot spots in the airport other than in the lounges. Your wait won't be super long. We've usually gone to the Am Ex club (gold card or higher required; it is more basic than most airline lounges I've been in). I think there are a couple of other clubs, such as Diners Club (?), outside security.

Fresh air around the airport?? Really? There is an observation platform, but not much to see if you're already going to be at a departure gate.

As noted, when you depart, assuming SAA departs from Terminal 2 (like United), you should be able to use the consolidted VIP lounge, used by departing international passengers of a number of airlines (if one is flying biz/first or otherwise has access). We used it when departing on US Airways. A few snacks, showers, and comfortable chairs. It's downstairs from the main departure area (once in the gate area, walk to the left to the small duty free store and then go down the stairs). It's next to a TAM "Gold" lounge.