1) Taxis, generally no. Restaurants and shops are variable. Exchange rate by using US$ cash isn't going to be particularly favorable now vs. the official exchange rate.

2) Any of the booths inside the airport are fine for a car service into the city. They are located just past customs inspection before entering the general circulation area. For the EZE-unfamiliar, I wouldn't bother figuring out how to locate an UBER, all of which are unmarked. Within the city, I've tried UBER a couple of times and it has been fine.

3) Without a link to what you're looking at, no idea.

4) In most of San Telmo, it is safe enough using your normal precautions. At night, try and keep it to the main streets (Defensa, Chile, Independencia, Paseo Colon) for your longer walking, and try to avoid the south side of the highway. (It passes above ground past Av. San Juan.) As for other parts of the city you may explore, just normal street smarts by day, and take taxis/uber between neighborhoods at night. No matter what you do, if you are by the Retiro train station, do not wander on the back side of it.